PUBLICATIONS:

Doctoral Dissertations:

Directed Ph.D. theses for: 

Barbara Osofsky (1964), full Professor, Rutgers University. 

Avraham Orenstein (1966), full Professor, Israel Inst. of Technology (TECHNION), Haifa, Israel 

William Caldwell (1966), full Professor, Chair, Math Dept., Univ. of North Florida, Jacksonville, Florida 

Victor Camillo (1970), full Professor, Univ. of Iowa, Iowa City, Iowa 

John H. Cozzens (1970), Senior Research Mathematician, and Program Director for Applied Math, National Science Foundation, Washington, D.C.

Ann Koski Boyle (1971), full Professor, University of Wisconsin, Milwaukee and Program Director for Algebra, National Science Foundation, Washington, D.C. 

Ranga Rao (1973), full Professor, Univ. of Aurangabad, India 

Saroj Jain (1973), Assoc. Professor, Indianapolis, Indiana, Butler State Univ.

Co-directed (with W. Vasconcelos) the Ph.D thesis of Leroy Hudson (1985), Professor, US Merchant Marine Academy Kingspoint, L.I. New York

External Examiner of Ph.D. Theses of: 

David Fields (McGill Univ.., Montreal,  Circa 1969) 

John Lawrence ( Carleton University., Ottawa, 1975) 

Mary Upham Wright (McGill Univ.., Montreal, Circa 1977) 

Dolors Herbera (Universitat Autònoma de Barcelona, Barcelona, 1992)

Books:

1. Lectures on injective modules and quotient rings, Springer Lecture Notes, #49, Heidelberg (1967), 149; rev.& expanded ed. of #23, incl. preface & 4 new chapters.

2. Algebra:  Rings, Modules, and Categories, I, XXII +565 pgs., Springer-Verlag, Grundlehren Math. Wiss Bd 190, Berlin, 1973.

3. Simple Noetherian Rings, (with J. H. Cozzens), Cambridge Tracts in Mathematics. Cambridge Univ. Press., NY & Cambridge, 1975.

4. Algebra II:  Ring Theory, Grundlehren Math. Wiss, Bd.191, Springer, Berlin (1976), XXI + 302 pp.

5. Algebra:  Rings, Modules and Categories I; new Russian edition of book #1, MIR Publishers, Moscow, 1976, 688 pp., illustrated.

6. Algebra II: Ring Theory, new Russian edition of book #4, MIR Publishers, Moscow (1979), 482 pgs, illustrated.

7. Algebra I: Rings, Modules and Categories, reprint of #49, corrected reprint (1981), XXV + 571 pgs with new Preface and Index of names added.

8. Injective Modules and Injective Quotient Rings, Lecture Notes in Pure & Applied Math., 72 Marcel Dekker, Inc., Basel and New York, 1982.

9. FPF Ring Theory: Faithful Modules and Generators of Mod-R (with S. Page), Lecture Notes of the London Math. Soc., 88, Cambridge  Univ. Press, Cambridge, 1984.

10. Classification of Commutative FPF Rings (with P. Pillay), Notas de Matematicas, Universidad de Murcia, Murcia, Spain, 1990.

11. Rings and Things and a Fine Array of Twentieth Century Associative Algebra, Surveys of the American Math. Soc., vol. 65, Providence, 1999, 2nd revised and enlarged edition, 2004.

Journals and Preceedings Papers:

1. Extensions of normal bases and completely basis fields, Trans. A.M.S., 85 (1957), 406-427.

2. Galois extensions in which every element with regular trace is a normal basis element , Proc. Amer. Math. Soc. 9 (1985), 222-229.

3. On conjugates in division rings, Canadian Journal of Math.,10 (1958), 374-380.

4. Rings with minimum conditions on principal ideals, Archiv der Mathematik, 10 (1959), 327-330.

5. Submodules of rings, Proc. Amer. Math. Soc, 10 (1959), 596-606.

6. Abelian Galois groups, Proc. Amer. Math. Soc, 10 (1959), 767-774.

7. Algebraic division ring extensions , Proc. Amer. Math. Soc., 11 (1960), 43-53.

8. Radical extension of rings , Proc. Amer. Math. Soc, 12 (1961), 274-283.

9. Zwei-elemente-erzeugung und endichkeit der dimension von divisionalgebren, Archiv der Mathematik, 11(1961), 405-406.

10. Rings with minimum condition on principal ideals, II , Archiv der Mathematik, 12 (1961), 179-182.

11. On Herstein's theorem concerning three fields , Nagoya Math. Jour, 15 (1961), 49-53.

12. Derivations and generations of finite extensions , Bulletin of the American Mathematical Society, 67 (1961), 550-553 (Comm. by Nathan Jacobson).

13. On a theorem of Tsen , Archiv der Mathematik, 12 (1961), 330-333.

14. Semialgebraic extensions of division algebras , J. Reine Angew. Math., 209 (1962), 144-162.

15. Strongly regular extensions of rings , Nagoya Math. Jour, 16 (1962), 1-12.

16. Intrinsic extensions of rings (with Yuzo Utumi), Pacific Journal, 14 (1964), 505-512.

17. On a new proof of Litoff's theorem (with Y. Utumi), Acta Math. Hungar, 14 (1964), 369-371.

18. Quasi-injective modules and their endomorphism rings (with Y. Utumi), Archiv der Mathematik.,15 (1964), 166-174.

19. Baer modules (with Yuzo Utumi), Archiv der Mathematik,15 (1964), 266-270.

20. On the noetherian prime rings (with Yuzo Utumi), Appendix B of Jacobson's revised colloquium book, Structure of Rings. Also, Trans.A.M.S.,114 (1965), 53-60.

21. Orders in simple artinian rings , Trans. A.M.S., 114 (1965), 61-64.

22. Simple noetherian rings , Bulletin of the American Mathematical Society., 70 (1964), 753-731.

23. Quotient rings and direct products of full linear rings (with Stephen U.Chase), Mathematische Zeitschrift, 88 (1965), 250-264.

24. Maximal quotient rings (with Yuzo Utumi), Proc. Amer. Math. Soc, 16 (1965), 1084-1089.

25. Rings with ascending condition on annihilators , Nagoya Math. Jour, 27 (1966), 179-191.

26. On Kothe rings , Math. Annalen, 164 (1966), 207-212.

27. General Wedderburn theorem , Bulletin of the American Mathematical Society, Res. announcement, 73 (1967), 65-67 (Comm. by N. Jacobson).

28. Direct sum representations of injective modules (with Elbert A. Walker), Jour. of Algebra, Academic Press, 5 (1967),    203-221.

29. A correspondence theorem for projective modules and the structure of simple noetherian rings , Bulletin of the American Mathematical Society, 77 (1971), 338-342.

30. Big decompositions of modules , Notices A.M.S., 18 (1971), 400.

31. Orders in semilocal rings, Research announcement , Bulletin of the American Mathematical Society,71 (1971), 338-342 (Comm. by H. Bass).

32. Modules finite over endomorphism rings , Proc of the Tulane Univ. Symp. in Ring Theory, New Orleans, Lecture Notes in Math., 246 (1972), 145-190.

33. A correspondence theorem for projective modules and the structure of simple noetherian rings , Symp. Math Istituto di Alta Matematica , 8 (1972), 309-345.

34. Galois subrings of Ore domains are Ore , Bulletin of the American Mathematical Society, 78 (1972), 1077-1080 (Comm. by Nathan Jacobson).

35. When are proper cyclics injective? ,Pacific Journal, 45 (1973), 97-112

36. On the structure of indecomposable injectives Modules , Comm. Algebra, 2 (1974), 559-571.

37. On a theorem of Chatters , Comm. Algebra, 3 (1975), 169-184.

38. Projective ideals in Cohen rings , Archiv der Mathematik, 26 (1975), 588-594.

39. Injective cogenerator rings and a theorem of Tachikawa, I , Proc. Amer. Math. Soc, 60 (1976), 25-30.

40. Galois extensions of commutative rings , Math. J. Okayama U, 18 (1976), 113-116.

41. On hereditary rings and Boyle's conjecture , Archiv der Mathematik, 27 (1976), 113-119.

42. Semiperfect Prufer rings and FPF rings , Israel Math. J., 26 (1977), 166-177.

43. Injective cogenerator rings and a theorem of Tachikawa, II , Proc. Amer. Math. Soc, 62 (1977), 15-18.

44. The basis theorem for modules:  a brief survey and a look to the future  , Proc. Antwerp Conf. in Ring Theory, 1977, Lecture Notes in Pure &  Applied Math., Marcel Dekker, Inc. (1978).

45. Injective quotient rings of commutative rings , Module Theory: Papers and problems from the special session, 1977, Lecture Notes in Math., 700 (1979), 151-203.

46. Bounded prime rings, pseudo-Frobenius rings, the Jacobson radical of a ring , Module Theory: Papers and problems from the special session, Lecture Notes in Math.,700 (1979), 218-223.

47. The genus of modules and generic families of rings , Antwerp Conf. in Ring Theory, 1978, Lecture Notes in Pure and Applied Math., Marcel Dekker, Inc. 51 (1979), 613-629.

48. Self-injective rings , Proc. Amer. Math. Soc, 77 (1979), 157-164.

49. Injective modules over Levitzki rings , Injective Modules and Injective Quotient Rings, Lect. Notes Pure Appl. Math. 72 Marcel Dekker, Inc. (1982), 1-69.

50. Injective quotient rings of commutative rings , Injective Modules and Injective Quotient Rings, Lect. Notes Pure Appl. Math. 72  Marcel Dekker, Inc. (1982), 71-105.

51. On the Galois theory of commutative rings I :  Dedekind's theorem on the independence of automorphisms revisited, in ``Algebraist's Homage" Yale symp. proc. honoring N.Jacobson, Contemp. Math.,13 (1982), 183-192.

52. Subrings of self-injective and FPF rings, in Advances in Non-commutative Ring Theory , Proc. of the Hudson Symp., 1981, Plattsburgh, Lecture Notes in Math., 951 (1982), 12-20.

53. Embedding modules in projectives , Proc. of the Hudson Symposium, Plattsburgh, 1981, Lecture Notes in Math., 951 (1982), 21-40.

54. Commutative FPF rings arising as split-null extensions , Proc. Amer. Math. Soc,  90 (1984), 181-185.

55. The structure of valuation rings , Journal of Pure and Applied Algebra, 31 (1984), 7-27.

56. Independent groups of automorphisms of commutative rings are quorite , Math. J. Okayama U., 25 (1984), 23-25.

57. The maximal regular ideal of self-injective and continuous rings splits-off , Archiv der Mathematik. 44 (1985), 511-521.

58. Book Review:  Jacobson, Nathan; Lectures in Abstract Algebra, Vol.\ III. D. van Nostrand, Princeton, 1964 (Math. Reviews, 30, #3087).

59. Book Review:  Jacobson, Nathan; Structure of Rings, A.M.S. Colloquium Publ. 37 (Rev. Ed.), Providence, 1964) (Math Reviews, 36, #5158).

60. Book Review:  Goodearl, Kenneth; Ring Theory, Nonsingular Rings and Modules, Marcel Dekker, Inc., New York-Basel, 1976 (Math Reviews, 55, #2970).

61. The structure of valuation rings II , Journal of Pure and Applied Algebra, 42 (1986), 37-43.

62. Linearly compact injective modules and a theorem of Vamos , Publicacions Matemàtiques, Universitat Autònoma de Barcelona (UAB), 30, (1986), 127-148.

63. Cozzens' domains are hereditary , Math. J. Okayama U, 28 (1986) 37-39.

64. On the Galois theory of commutative rings II: Automorphisms induced in residue class rings , Canadian Journal of Math., 39 (1987), 1025-1037.

65. Rings with zero intersection property for annihilators: zip rings , Publicacions Matemàtiques., Universitat Autònoma de Barcelona(UAB), 33 (1989) 329-338.

66. Polynomial rings over Jacobson-Hilbert rings , Publicacions Matemàtiques, Universitat Autònoma de Barcelona (UAB), 33 (1989), 85-97.

67. Embedding torsionless modules in projectives ,Publicacions Matemàtiques, Universitat Autònoma de Barcelona (UAB), 34 (1990), 379-387.

68. Annihilator ideals, associated primes and Kasch-McCoy quotient rings of commutative rings, Robert Warfield Commemorative Issue, , Comm. Algebra 19 (1991), 1867-1892 (Comm. by Pere Menal, Editor).

69. Book Review:  Commutative Rings with Zero Divisors by James Huckaba, Marcel Dekker, Inc.New York and Basel, 1989 (Bulletin of the American Mathematical Society 1990).

70. Counter-example to a conjecture of Johns (with Pere Menal), Proc. Amer. Math. Soc116 (1992), 21-26 (Comm. by M. Auslander).

71. Book Review:  Rings and Categories of Modules, by F.W. Anderson and K.R.Fuller, Springer-Verlag, 1974, Math. Revs. 54, No. 5281.

72. Finitely embedded commutative rings , Proc. Amer. Math. Soc 112 (1991), 657-659 (Comm. by L. J. Ratliff, Jr.).

73. Defeat of the FP²F Conjecture:  Huckaba's Example , Proc. Amer. Math. Soc 116 (1992), 5-6 (Comm. by L. J. Ratliff,Jr.).

74. Self-injective Von Neumann regular subrings and a theorem of Pere Menal ,Publicacions Matemàtiques, Universitat Autònoma de Barcelona, 36 (1992), 541-567.

75. Polynomial rings over Goldie-Kerr commutative rings ,  Proc. Amer. Math. Soc 120 (1994), 989-993 (Comm. by Eric Friedlander).

76. The structure of Johns rings (with Pere Menal), Proc. Amer. Math. Soc, 120 (1994), 1071-1081 (Comm. by L. W. Small).

77. Rings whose modules have maximal submodules, Publicacions Matemàtiques. 39 (1995) 201--214.

78. A new duality theorem for semisimple modules and characterization of Villamayor rings, (with Pere Menal), Proc. Amer. Math. Soc., 38  (1995), 1635-1637 (Comm. by L. W. Small).

79. Polynomials over Goldie-Kerr commutative rings II , Proc. Amer. Math. Soc.124 (1996), 341-344 (Comm. by W. V. Vasconcelos).

80. Locally perfect commutative rings are those whose modules have maximal submodules, Comm. Algebra. 23 (1995) 4885--4886 (Comm. by W. V. Vasconcelos).

81. A new characterization of von Neumann regular rings and a theorem of Shamsuddin, Publicacions Matemàtiques. 40 (1996) 383-385.

82. Rings with few zero divisors are those with semilocal Kasch quotient rings, Houston J. Math, 22 (1996) 687-690.

83.  FP-injective quotient rings and elementary divisor rings (with Alberto Facchini), in Commutative Ring Theory (P-J Cahen et al, eds) Proceedings of the Fés International Conference II; Lecture Notes in Pure and Applied Math., vol. 125, pp. 293-302, Marcel Dekker, Inc.., New York-Basel, (1997).

84. Tensor products and endomorphism rings of linearly compact modules (with Dolores Herbera),Comm. Algebra 25 (1997) 1215-1256.

85. Minimal cogenerators over Osofsky and Camillo rings , in Advances in Ring Theory (S. K. Jain and T. Rizvi, eds.) Birkhäuser Verlag Boston, 1997, pp. 105-118.

86. Commutative rings with acc on irreducible ideals in Abelian Groups, Module Theory, and Topology, Proc. Conf. in Honor of A. Orsatti's 60th Birthday, Padova, June 1997; Lecture Notes in Pure and Appl. Math., vol. 201, Marcel Dekker, Inc., Basel and New York, 1998, pp. 157-178.

87. Quotient finite dimensional modules with acc on subdirectly irreducible submodules are Noetherian, Comm. Algebra, 27 (1999), 1807-10.

88. Note on residually finite rings, Comm. Algebra, 28 (2000) 4223-26.

89. Associated primes in commutative polynomial rings, Comm. Algebra, 28 (2000) , 3983-86.

90. Indecomposable injective modules and a theorem of Kaplansky, Comm. Algebra, 30 (2002), 5875-89.

9l. (with Dinh Van Huynh) When self-injective rings are QF: A report on a problem, Journal of Algebra and Applications, 1 (2002), 75-105.

92. Coherent rings and annihilators conditions in matrix and polynomial rings, Handbook of Algebra, M. Hazewinkel, Ed., vol. 3, Elsevier B.V., Amsterdam, 2003.

93. When cyclic modules have sigma injective hulls, Comm. Algebra, 31 (2003), 4161-4173.

94. Dedekind finite rings and a theorem of Kaplansky, Comm. Algebra 31(2003), 4175-4178.

96. Factor rings of pseudo-Frobenius rings, J. Algebra and its Applications, 5 (2006) 847-854; Erratum, ibid., 2007

97. The Sun Shines Bright: A Kentucky Boyhood in the Great Depression and World War II, Xlibris, Philadelphia, 2007 (telephone: 1-888-795-4274, or on the Web at Xlbris.com

98. The Sun Shines Bright: Index and Glossary, Memories of the 60-th Anniversary Reunion of Holmes High School Class of 1995, on the Mark Twain Riverboat on the Ohio River at Covington, KY, June 4, 2005, and Memories of the Zanesville Ohio University Conference in Honor of Carl Faith's 80th and Barbara Osofsky's 70th Birthday, June 15-17, 2007. Xlibris, Philadelphia, 2008

Conference Proceedings:

1. Module Theory (C. Faith and S. Weigand Eds.), Lecture Notes in Math., 700 (1979), Springer-Verlag (edited), 239 pages.

Preprints:

1.  Here we go round the mulberry bush:  How numbers grow like berries.

Invited Papers:

Vol. of Archiv der Mathematik commemorating R. Baer's 60th birthday anniversary (2 papers with Y. Utumi), 1964

Vol. of Nagoya Math. Jour, in memory of T.Nakayama, 1966

Vol. of Mathematische Zeitschrift celebrating G. Kothe's 60th birthday anniversary, 1966

1977 Antwerp Ring Theory Conference Proceedings 

1981 Proceedings of the Hudson Symposium, Plattsburgh

"Algebraist's Homage", N. Jacobson on his 70th birthday, Contemp. Math 13 (1982)

Invited paper in the Emmy Noether Centenary Celebration issue of the Journal of Pure and Applied Algebra, vol. 31 (1984)

Invited paper in the Robert Warfield Memorial volume of Communications in Algebra,  vol. 19 (1991)

Invited paper in the Pere Menal Memorial volume (C.Perelló, Ed.) Publicacions Matemàtiques, vol. 36 (1992)

Invited paper for Orsatti's 60th Birthday Conf. Proceedings (1997)

Papers Presented to Mathematical Congresses:

International Congress of Mathematicians, Edinburgh, 1958

International Congress of Mathematicians, Stockholm, 1962

Poems:

Selected Poems PDF file