Manfred H. Dugas
(My homepage, under construction!!)
In case you want to see a picture of me in a suit and tie,
and my whole family all dressed up:
My daughter Diana's wedding May 22, 2005.
MANFRED H. DUGAS
Address: Department of Mathematics
B.U. Box 7328
Waco, Texas 76798
Citizenship: German, Permanent Resident of the United States.
Marital Status: Married, two children
Education: M.S.: 1975 Mathematics
University of Kaiserslautern, Germany
Ph.D.: 1974, Mathematics
University of Kaiserslautern, Germany
Habilitation: 1979, University of Essen, Germany
Fields of Research Interest: Theory of Abelian groups, rings, and modules
1990- Professor, Department of Mathematics,
Baylor University, Waco, Texas
1987-90 Associate Professor, Department of Mathematics
Baylor University, Waco, Texas
1985-87 Associate Professor, Department of Mathematics
University of Colorado at Colorado Springs
1984-85 Visiting Associate Professor
University of Colorado at Colorado Springs
1976-84 Assistant Professor of Mathematics
University of Essen, Germany
1975 DFG ( = German NSF) Research Fellowship
Membership: Member of the American Mathematical Society
1. International Conference on Abelian Groups, Oberwolfach, Germany, 1980: “Strongly ?-free modules in L.”
2. International Conference on Abelian Groups, Honolulu, HI, 1982: “On mixed Abelian Groups.”
3. A series of lectures at the University of Padova, Italy, Fall 1982, on “Endomorphism Rings.”
4. International Conference, Udine, April 1984: “On radicals, torsion theories and large cardinals.”
5. DMV (= German AMS) meetings, Fall 1983 and Fall 1981: “Constructing large modules” and “On rings with large indecomposable modules.”
6. International Conference on Abelian Groups, Oberwolfach, West Germany, 1985: “Fields with prescribed automorphisms.”
7. Presented a paper at the annual AMS meeting, January 1987, in San Antonio.
8. I was invited to give colloquium talks at Auburn University, AL, the University of Mississippi, MS, the University of Florida, Gainsville, FL, the University of Connecticut, Storrs, CT, Wesleyan University, Middletown, CT, the University of California at Irvine, Wayne State University, Detroit, MI, University of Arizona, Tucson, AZ., University of Houston, Trinity University, and Essen University, Germany.
9. A talk in the special session on Abelian groups, Annual AMS meeting, January 1988, Atlanta, GA.
10. International Conference on Abelian Groups, Oberwolfach, W. Germany, 1989: “Applications of abelian groups.”
11. “On a class of p-groups,” Colloquium talk, University of Essen, Germany, June 1990.
12. “On a class of Abelian p-groups,” presentation at the Twenty-First Annual USL Math Miniconference, Lafayette LA, October 1990.
13. “Construction of Groups,” 862nd Meeting of the AMS, Irvine, CA, November 1990.
14. “Uncountable Butler Groups,” Seminar talk given at the U. of Colorado, Colorado Springs, December 1990.
15. “Classification of ACD Groups”, presentation at the Conference on Methods in Module Theory, Colorado Springs, June 1991.
16. “E-uniserial Abelian Groups”, presentation at the Conference on Abelia n Groups, Curacao, August 1991.
17. “Butler Groups of infinite rank” presentation given to the Graduate College of Essen University, Essen, Germany, July 1992.
18. “Classification of Finite Rank Butler Groups”, a four week seminar given to the Mathematics Department of the University of Padova, Padova, Italy, July 1993.
19. “Near Isomorphisms of ACD Groups”, talk given at the International Conference on Abelian Group Theory in Oberwolfach, Germany, August 1993.
20. “Butler Groups and Representations of Posets” invited talk given at the International Conference on Abelian Groups and Modules, Colorado Springs, August 95.
21. “Fast vollständig zerlegbare Gruppen mit wenigen Typen”, Colloquium talk at Essen University, Essen, Germany, July 1996.
22. “BCD-Groups with Type Set (1,2)”, presentation at the International Conference on Abelian Groups and Modules, Dublin Institute of Technology, Dublin, Ireland, August 1998.
23. “Infinite Combinatorics in Algebra” invited talk at the Conference on Infinite Combinatorics and Set Theory, (European Science Foundation), Hattingen, Germany, July 1999.
24. “M-Free Abelian Groups”, Colloquium talk, University of Colorado at Colorado Springs, March 2001.
25. “Completely Decomposale Abelian Groups with a Distinguished CD Subgroup”, talk given at the Second Honolulu Conference on Abelian Groups and Modules, August 2001.
26. “Self-Free Modules and E-rings”, Colloquium talk at the University of Houston, March 2002.
27. “Self-Free Modules”, talk given at the Algebra Conference – Venezia 2002, Venice, Italy, June 2002
28. “Self-Free Abelian Groups, talk given at the conference: Algebra-Geometry; An International Conference in Memory of Reinhold Baer, Hattingen, Germany, July 2002.
29. “A-Rings”, talk given at the Weekend Algebra Conference at Florida Atlantic University, November 2003
30. “Localizations of Abelian Groups”, talk given at the Abelian Groups, Rings and Modules Conference, Auburn University, September 2004.
I had the following grants from the National Science Foundation funding my research (Summer salary and travel):
“Butler Groups of Infinite Rank”, 1987 and 1988, $17,100, DMS-8896186.
“Endomorphisms of Groups and Modules”, 1989 and 1990, $36,700, DMS-8900350.
“Invariants and endomorphisms of rings and Modules” (with D. Arnold), 1991 and 1992, $102,000, DMS-910100.
NSF Grant to fund a five day workshop “Set Theoretic Methods in Algebra” held at Baylor University in May 1990, $6,800.
(“Torsion-free Abelian Groups and modules with distinguished submodules”, 1993 and 1994, (with D. Arnold) $107,881, submitted to the NSF in Fall 1992; did not receive funding.)
“Classification of Abelian Groups and Modules”, 1994 and 1995, (with D. Arnold), $103,389, submitted to the NSF in Fall 1993. Status: Funded at a 50% level.
(“Generic Butler Groups and Representation Type”, 1997/98 (with D. Arnold), $120,870 submitted to NSF in Fall 1996, did not receive funding.)
(“Categories of Butler Groups and Representations”, 1998/99, (with D. Arnold), submitted to the NSF in Fall 1997, did not receive funding.)
(“Localizations of Abelian Groups”, 2004/05, submitted to the NSF, did not receive funding.)
Over the last ten years I taught the following classes, by level:
Calculus I and II (utilizing a graphing calculator (TI 86)
Linear Algebra (utilizing the TI 86)
Euclidean and Non-Euclidean Geometry
Graduate Algebra I and II
I also directed numerous independent reading classes for individual students needing additional hours. Here are some of the topics: Axiomatic set theory, coding theory, rings and modules, homological algebra, E-modules. Topics in Abelian group theory
I served as adviser for Master’s Theses/Projects for the following students:
(Until 2001/2002, we didn’t have a Ph.D. program.)
Mouser, Mary Alice, On Z/p^2Z-modules with distinguished submodules, May 1993
Reiner, David R., Burst error correction, 1996
Guyton, Robert M., Centralizers of matrices, 1997
Morse, Misty, Complete Latin squares, 1997
Maddox, Amy, Endomorphism rings of some representations of critical posets, 1998
Kirchmer, Janie, A model of the hyperbolic plane, 1998
Wade, Rachel, On the existence of square roots of matrices, August 1999
DaCunha, Jeff, Freeness of modules relative to a single module, December 2001.
Conley, Kelly, The Golden Ratio, May 2003
I am currently working with Joshua Buckner, a Ph.D. candidate.
1. M. Dugas, Characterisierungen endlicher desarguesscher uniformer Hjelmslev-Ebenen, Geo Ded 3 (1974), 295-342.
2. M. Dugas, Eine Kennzeichnung der endlichen desarguesschen Hjelmslev-Ebenen, Arch. Math.27 (1976), 556-560.
3. M. Dugas, Moufang – Hjelmslev-Ebenen, Arch. Math. 28 (1977), 318-322.
4. M. Dugas, Verallgemeinerte Andre-Ebenen mit Epimorphismen auf Hjelmslev-Ebenen, Geo. Ded. 8 (1979), 105-123.
5. M. Dugas and R. Göbel, Algebraisch kompakte Faktorgruppen, J. R. Angew, Math 307/308 (1979), 341-354.
6. M. Dugas and R. Göbel, Die Strucktur kartesischer Produkte ganzer Zahlen modulo kartesischer Produkte ganzer Zahlen, Math. Z. 168 (1979), 15-21.
7. M. Dugas, Der Zusammenhang zwischen Hjelmslev-Ebenen und H. Verbanden, Mitt. Math. Gesellschaft, Hamburg, 10 (1980), 709-749.
8. M. Dugas, Die Kollineationsgruppe verallgemeinerter Andre-Ebenen mit Homologien, Math. Z. 175 (1980), 87-95.
9. M. Dugas and R. Göbel, Quotients of reflexive modules, Fund. Math. 114 (1981), 17-28.
10. M. Dugas, Fast freie abelsche Gruppen mit Endomorphismenring Z. J. Algebra 71 (1981), 314-321.
11. M. Dugas and B. Zimmermann-Huisgen, Iterated direct sums and products of modules, Springer LNM 874 (1981), 179-193.
12. M. Dugas and R. Göbel, Every cotorsion-free ring is an endomorphism-ring, Proc. Lond. Math Soc. (3) 45 (1982), 319-336.
13. M. Dugas and R. Göbel, On endomorphism rings of primary Abelian groups, Math. Ann. 261 (1982), 359-385.
14. M. Dugas and R. Göbel, Every cotorsion-free algebra is an endomorphism algebra, Math. Z. 181 (1982), 452-470.
15. M. Dugas and G. Herden, Arbitrary torsion classes and almost free Abelian groups, Israel J. Math. 44 (1983), 322-334.
16. M. Dugas and G. Herden, Arbitrary torsion classes of Abelian groups, Comm. Alg. 11 (1983), 1455-1474.
17. M. Dugas, On the existence of large mixed modules, Spring LNM 1006 (1982/83), 412-424.
18. M. Dugas and R. Göbel, On endomorphism rings of Abelian groups II, Springer LNM 1006 (1983), 400-411.
19. M. Dugas, R. Göbel, and B. Goldsmith, Representation of algebras over a complete discrete valuation ring, Quart. J. (Oxford) (2), 35 (1984), 131-146.
20. M. Dugas and R. Göbel, Torsion-free Abelian groups with prescribed finitely topologized endomorphism ring, Proc. Amer. Math. Soc. 90 (1984), 519-527.
21. M. Dugas and R. Göbel, On radicals and products, Pac. J. Math 118 (1985), 79-104.
22. M. Dugas and R. Göbel, Countable mixed Abelian group with very nice full-rank subgroups, Israel J. Math. 51 (1985), 1-12.
23. M. Dugas and R. Göbel, On almost ?-cyclic Abelian p-groups in L, Abelian Groups and Modules, Proceedings of the Udine Conference, 1984, CISM Courses and Lectures 287, 87-105.
24. M. Dugas, On reduced products of Abelian groups, Rend. Sem. Math. Univ. Padova, 73 (1985), 41-47.
25. M. Dugas and R. Göbel, Endomorphism rings of separable torsion-free Abelian groups. Houston J. Math, 11 (1985), 471-483.
26. M. Dugas, A. Mader and C. Visonhaler, Large E-rings exist, J. Algebra, 108 (1987), 88-101.
27. M. Dugas, On modules over valuation rings with a nil radical, Proceedings of the Third OW-Conference on Abelian Groups 1985, Gordon and Breach, 457-509.
28. M. Dugas and R. Göbel, Field Extensions in L, Proceedings of the Third OW-Conference on Abelian Groups 1985, Gordon and Breach, 509-529.
29. M. Dugas and R. Vergohsen, On socles of Abelian p-groups, Rocky Mountain J. Math., 18 (1988), 733-752.
30. M. Dugas and K. M. Rangaswamy, On torsion-free Abelian K-groups., Proc. Amer. Math. Soc. 99 (1987), 403-408.
31. M. Dugas, T.H. Fay and S. Shelah, Singly cogenerated annilhilator classes, J. Algebra, 109 (1987), 127-137.
32. M. Dugas and R. Göbel, All infinite groups are Galois groups over any field, Trans. Amer. Math. Soc. 304 (1987), 355-384.
33. M. Dugas, J. Irwin and S. Khabbaz, Countable rings as endomorphism rings, Quart. J. Math. Oxford (2), 39 (1988), 201-211.
34. M. Dugas, On the radical of some endomorphism rings, Proc. Amer. Math. Soc. 102 (1988), 823-826.
35. M. Dugas, On some subgroups of infinite rank Butler groups, Rend. Sem
Math. Univ. Padova, 79 (1988), 153-161.
36. M. Dugas and K.M. Rangaswamy. On Butler groups of infinite rank, Trans. Amer. Math Soc., 305 (1988), 129-14
37. M. Dugas and J. Irwin, On basic subgroups of ?Z, Comm. Alg. 19 (11) (1990), 2907-2921.
38. M. Dugas and S. Shelah, E-transitive groups in L, Contemporary Math., 87 (1989), 191-200.
39. M. Dugas and J. Hausen, Torsion-free E-uniserial groups of infinite rank, Contemporary Math., 87 (1989), 181-190.
40. M. Dugas and E. Oxford, Preradicals induced by torsion-free groups, Comm.
Algebra, 17 (1989), 981-1002.
41. M. Dugas, P. Hill, and K. M. Rangaswamy, Infinite rank Butler groups II, Trans. Amer. Math. Soc. 320 (1990), 643-664.
42. M. Dugas and J. Irwin, On pure subgroups of cartesian products of integers, Results in Math, 15 (1989), 35-52.
43. M. Dugas and R. Göbel, Outer automorphisms of groups, Ill. J. Math.
44. M. Dugas and R. Göbel, On locally finite p-groups. J. Algebra. 159 (1993), 115-138.
45. M. Dugas and R. Göbel, Torsion-free nilpotent groups and E-modules, Archiv. d. Math. 54, (1990), 340-351.
46. M. Dugas and B. Thomé, On Butler groups of countable rank and vector spaces with distinguished subspaces, J. Algebra, 138 (April 1991), 249-272.
47. M. Dugas and B. Thomé, The functor Bext under the negation of CH, Forum Mathematicum 3 (1991), 23-33.
48. M. Dugas and R. Göbel, Abelian p-groups with a prescribed chain of subgroups, Israel J. Math. 79 (1992), 153-159.
49. M. Dugas and R. Göbel, Nilpotent groups of class two, Trans. Amer. Math. Soc. 332 (1992), 633-646.
50. M. Dugas, J. Hausen and J. Johnson, Rings who additive endomorphisms are multiplicative, Bull. Austral. Math. Soc. 45 (1992), 91-103.
51. M. Dugas, Large E-modules exist, J. Algebra, 142 (October, 1991). 405-413.
52. M. Dugas and J. Irwin, On a class of abelian p-groups, Forum Math 4 (1992), 147-158.
53. M. Dugas and J. Irwin, On thickness and decompositions of abelian p-groups, Israel J. Math. 79 (1992), 153-159.
54. M. Dugas and E. Oxford, Near isomorphism invariants for some almost completely decomposable groups, Lecture Notes in Pure and Applied Mathematics (Marcel Dekker, Inc.), vol. 146 (1993), 129-150.
55. M. Dugas, On countable torsion-free abelian groups with trivial Z-dual, Proc. Royal Irish Acad. 92A (1992), 85-87.
56. M. Dugas and B. Olberding, E-uniserial abelian groups, in “Methods in Module Theory”, Lecture Notes in Pure Appl. Math., Marcel Dekker, vol 140, (1993), 75-86.
57. M. Dugas and K. M. Rangaswamy, Separable pure subgroups of completely decomposable groups, Arch. Math. 58 (1992), 332-337.
58. M. Dugas and T. Faticoni, Cotorsion-free abelian groups that are cotorsion as modules over their endomorphism rings, Lecture Notes in Pure and Applied Mathematics (Marcel Dekker, Inc.), vol. 146, 1993, 111-127.
59. M. Dugas and R. Göbel, Prescribing groups as automorphism groups of fields, Manuscripta Math. 85, (1994), 227-242.
60. M. Dugas, R. Göbel and W. May, Free modules with two distinguished submodules, Comm. Alg. 25(11) (1997), 3473-3481.
61. D. Arnold and M. Dugas, Representations of finite posets and near-isomorphism of finite rank Butler groups, Rocky Mount. J. Math. 25 (1994), 591-609.
62. D. Arnold and M. Dugas, Butler groups with finite type sets and free groups with distinguished subgroups, Comm. Alg. 21(6) (1993), 1947-1982.
63. D. Arnold and M. Dugas, Block rigid almost completely decomposable groups and lattices over multiple pullback rings, J. Pure Applied Alg. (1993), 105-121.
64. D. Arnold and M. Dugas, Indecomposable modules over Nagata valuation domains, Proc. Amer. Math. Soc. 122, (1994), 689-696.
65. M. Dugas and R. Göbel, Applications of Abelian groups and model theory to algebraic structures, “Infinite Groups”, Walter de Gruyter & Co, Berlin, 1995, 41-62.
66. D. Arnold and M. Dugas, Locally free finite rank Butler groups and near isomorphism, Abelian Groups and Modules, Kluwer, Boston, 1995, 41-48.
67. M. Dugas and R. Göbel, Automorphism groups of fields II, Comm. in Algebra, 25(12) (1997), 3777-3786.
68. M. Dugas and R. Göbel, Endomorphism rings of B2-groups of infinite rank, Israel J. Math. 101 (1997), 141-156.
69. D. Arnold and M. Dugas, A survey of Butler groups and the role of representations, Abelian Groups and Modules, Lecture Notes in Pure and Applies Mathematics, vol. 182, Marcel Dekker, 1996, 1-14.
70. M. Dugas and R. Göbel, Classification of modules with two distinguished pure submodules and bounded quotients, Results in Math. vol 30, 1996, 264-275.
71. D. Arnold and M. Dugas, Representation type of finite rank Butler groups, Colloquium Math. 74(2), 1997, 299-320.
72. D. Arnold and M. Dugas, Representation type of finite rank almost completely decomposable groups, Forum Mathematicum 10 (1998), 729-749.
73. D. Arnold and M. Dugas, Finite rank Butler groups with small typesets, in: Abelian Groups and Modules, Trends in Mathematics, Birkhauser, 1999, 107-120.
74. M. Dugas, BCD-groups with type set (1,2), Forum Mathematicum 13, (2000), 143-148.
75. M. Dugas and R. Göbel, Automorphisms of geometric lattices, Algebra Universalis 45(4) (2001), 425-433.
76. D. Arnold and M. Dugas, Co-purely indecomposable modules over discrete valuation rings. J. of Pure and Applied Algebra, 161 (2001), 1-12.
77. D. Arnold and M. Dugas and K. M. Rangaswamy, Finite rank Butler groups and torsion-free modules over a discrete valuation ring, Proc. Amer. Math. Soc. 129(2), (2001), 325-335.
78. M. Dugas, S. Feigelstock, and J. Hausen, M-free Abelian groups, Rocky Mountain J. of Math., 32, no. 4, (2002), 1367-1382.
79. M. Dugas and S. Feigelstock, Nil R-mod Abelian groups, Math. Proc. Royal. Irish Acad. 102A (2002), no.1, 107-113.
80. M. Dugas and K. M. Rangaswamy, Completely decomposable abelian groups with a distinguished cd subgroup, Rocky Mountain J. of Math. 32, no. 4, (2002), 1383-1395.
81. M. Dugas and S. Feigelstock, Self-free modules and E-rings, Communications in Algebra 31, (2003), 1387-1402.
82. D. Arnold, M. Dugas, K.M. Rangaswamy, Torsion-free modules of finite rank over a discrete valuation ring, Journal of Algebra 272, (2004), 456-469.
83. M. Dugas and K. M. Rangaswamy, Stacked bases theorem for Butler groups, Forum Mathematicum 16, (2004), 223-230.
84. M. Dugas and S. Feigelstock, Additive groups of zero square rings, Acta Mathematica Hungarica 107 (1-2), (2005), 61-70.
85. M. Dugas and S. Feigelstock, A-rings, Colloquium Mathematicum, 96, no. 2, (2003), 277-292.
86. M. Dugas and C. Vinsonhaler, Two-sided E-rings, Journal of Pure and Applied Algebra 185, (2003), 87-102.
87. M. Dugas, AA-rings, Communications in Algebra 32, No. 10, (2004), 3853-3860.
88. M. Dugas and S. Feigelstock, AE-rings, Rend. Sem. Mat. Univ. Padova 111, (2004), 239-246.
89. M. Dugas, Localizations of torsion-free abelian groups, J. of Algebra 278, (2004), 411-429.
90. M. Dugas and S. Feigelstock, Co-minimal abelian groups, Houston Journal of Mathematics 31, (2005), 637-648.
91. M. Dugas, Localizations of torsion-free abelian groups II, Journal of Algebra 284, (2005), 811-823.
92. M. Dugas and C. Maxson, Quasi-E-locally cyclic torsion-free abelian groups,
Proc. Amer. Math. Soc. 133, (2005), 3447-3453.
93. J. Buckner and M. Dugas, Co-local subgroups of abelian groups, in: Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure and Applied Math., 249, Taylor & Francis/CRC Press, pp. 25-33, 2006 (Accepted Feb. 2005).
94. M. Dugas, Co-local subgroups of abelian groups II, to appear in the Journal of Pure and Applied Algebra. (Accepted Oct 2005)
95. J. Buckner and M. Dugas, Quasi-Localizations of Z, to appear in the Israel Journal of Mathematics, accepted February 2006.
96. J. Buckner and M. Dugas, Left rigid rings, submitted.
M. Dugas and R. Göbel, Zassenhaus rings.