Publications


1. Thesis, Right Alternative Rings, (1969), University of Iowa.

2. A Note on Modules and Radicals, Proc. Amer. Math. Soc. 19 (1969), 1385-1386 (refereed).

3. (-1,1) Rings, Proc. Amer. Math. Soc. 22 (1969), 367-374 (refereed).

4. (-1,1) Algebras, Proc. Amer. Math. Soc. 24 (1969), 24-28 (refereed).

5. Right Alternative Rings with Idempotents, J. Algebra 17 (1971), 303-309, (refereed).

6. Nil Semi-Simple (-1,1) Rings, J. Algebra 22 (1972), 442-450, (refereed).

7. On the Andrunakievich Lemma for Alternative Rings, J. Algebra 22 (1973), 243-256, (with 
M. Slater), (refereed).

8. Alternative Rings without Nilpotent Elements, Proc. Amer. Math. Soc. 42 (1974), 373-376, (refereed).

9. The Characterization of (-1,1) Rings, J. Algebra 30 (1974), 236-258, (refereed).

10. Generalization of Right Alternative Rings, Trans. Amer. Math. Soc. 207 (1975), 143-161, (with 
G. M. Piacentini) (refereed).

11. Generalized Right Alternative Rings, Pacific J. 60 (1975), 90-102, (refereed).

12. Quotient Rings from Right Ideals, Port. Math. 40 (3) (1981), 311-312, (refereed).

13. A Note on Generalizing Alternative Rings, Proc. Amer. Math. Soc. 55 (1976), 6-8, (with 
G. M. Piacentini) (refereed).

14. Semi-Prime Generalized Right Alternative Rings, J. Algebra 43 (1976), 14-27, (with 
G. M. Piacentini), (refereed).

15. Alternator and Associator Ideal Algebras, Trans. Amer. Math. Soc. 229 (1977), 87-109, (with D. Floyd and G. M. Piacentini) (refereed).

16. Simple ( ,
) Algebras are Associative,
 J. Algebra 47 (1977), 52-76, (with G. M. Piacentini), 
(refereed).

17. Processing Identities by Group Representation, Computers in Non-associative Rings and Algebras, Academic Press 1977, 13-40. Edited by R. E. Beck and B. Kolman (conference proceedings) (refereed).

18. Applying Group Representation to Non-Associative Algebras, Ring Theory V. (25) Marcel Dekker 1977, 133-141. Edited by S. K. Jain (conference proceedings) (refereed).

19. A Generalization of Anti-Commutative Rings Arising from 2-Varieties, Communications in Algebra (11)(1978), 1109-1114 (refereed).

20. Alternators of a Right Alternative Algebra, Trans. Amer. Math. Soc., 242 (1978), 141-156 (refereed).

21. Derivation Alternator Rings with Idempotent, Trans. Amer. Math. Soc. 258 (1980), 245-256, (with H. Smith)(refereed).

22. Special Jordan Identities, Communications in Algebra, 7 (16)(1979), 1759-1793, (refereed).

23. Alternative Rings with Idempotent, J. Algebra, 64 (1980), 325-335, (with E. Kleinfeld and H. Smith) (refereed).

24. Flexible Derivation Alternator Rings, Communications in Algebra 8 (20)(1980), 1997-2014, (with L. Hogben and H. Smith) (refereed).

25. Exhaustive Checking of Sparse Algebras, J. Algorithms 2 (1981), 44-49, (with L. Hogben) (refereed).

26. Generalized Alternative and Malcev Algebras, Rocky Mt. J. 12 (1982), 367-373 (with H. Smith) (refereed).

27. The Alternator Ideal of Right Alternative Rings, Bulletin of the Iranian Mathematical Society, 9 (1) (Serial No. 16): 15-20, 1981, (refereed).

28. Nil-Semi-Simple Locally (-1,1) Rings, Bulletin of the Iranian Mathematical Society, 9(1) (Serial No. 16): 11-14, 1981, (refereed).

29. Right Alternative Alternator Ideal Algebras, Comm. in Algebra, 11 (6)(1983), 633-670, (with 
G. M. Piacentini), (refereed).

30. Centers of Alternative Rings, J. of Algebra, June 1983, 90 (1984), 247-250, (refereed).

31. Degree Three Identities, Communications in Algebra, 12 (19), (1984), 2349-2399, (with G. Maria Piacentini), (refereed).

32. Semiprime Locally (-1,1) Rings with Minimal Conditions, Algebras, Groups and Geometries 2 (1985), 26-52, (with H. F. Smith), (refereed).

33. Right Alternative Algebras and Alternators, Bulletin of Iranian Math. Soc., 12 (1 and 2), 47-71, 1985, (with G. M. Piacentini), (refereed).

34. Simple Locally (-1,1) Nil Rings, J. Algebra 101 (1986), 262-272 (with H. F. Smith), (refereed).

35. A Note on the Analogue of Oppenheim's Inequality for Permanents, Linear Algebra and Applications, 94 (1987), 109-112 (with R. J. Gregorac), (refereed).

36. Degree Four Identities not Implies by Commutativity, Communications in Algebra, 16 (1988) 339-356 (with L. Carini and G. M. Piacentini), (refereed).

37. Almost Jordan Rings, Proc. Amer. Math. Soc., 104 (1988), 343-348, (with L. Peresi), (refereed).

38. A Computational and Graph Theoretic Approach to Nonassociative Algebras, Congressus Numerantium, 62 (1988), 241-258 (with D. J. Pokrass), (refereed).

39. Counterexamples in Non Associative Algebra, Algebras, Groups and Geometries5 (1988), 109- 128 (with L. Peresi), (refereed).

40. A Practical Solution for a Large Sparse Matrix, Software--Practice and Experience18 (1988), 3, 279-283, (with D. J. Pokrass), (refereed).

41. Verification of Non-Identities in Algebras, Proceedings of 1988 International Symposium on Symbolic and Algebraic Computation, P. Gianni (Ed.), Lecture Notes in Computer Science 358 (1989), 496-507 (with D. J. Pokrass), (refereed).

42. Semi-Prime Bernstein Algebras, Arch. Math. 52 (1989), 539-543 (with L. Peresi), (refereed). 

43. The Andrunakievich Lemma for Alternative Rings, Algebras, Groups, and Geometries, (1989), 55-64, (refereed).

44. Complexity and unsolvability properties of nilpotency, SIAM Journal of Computing, 19 (1990), 
32-43, (with D. P. Jacobs), (refereed).

45. On kth-Order Bernstein Algebras and Stability at the k + 1 Generation in Polyploids. IMA Journal of Mathematics Applied in Medicine and Biology, 7 (1990), 33-40, (with L. Peresi, P. Holgate), (refereed).

46. Bernstein Algebras given by symmetric bilinear forms, Lin. Alg. and Applications, 145 (1991), 213-219, (with L. Peresi), (refereed). 

47. Proofs for Non-identities Using Characteristic Functions, Congressus Numerantium, 78 (1990), 123-134, (with D. P. Jacobs), (refereed).

48. A Dynamic Programming Method for Building Free Algebras, Computers and Mathematics with Applications, 22 (1991), 12, 61-66, (with D. Pokrass Jacobs).

49. Computer Algorithms Based on Induction for Creating Identities of Higher Degrees, in Mechanics and Nonpotential Interactions Part I, Hadronic Nova Science Publishers, Inc., 1993.

50. On Rings in the Join of Associative and Commutative, J. Algebra 149 (1992), 528-537, (with 
E. Kleinfeld and H. Smith).

51. Digitizing Sum Graphs over the Reals, Caribbean Journal of Mathematical and Computing Sciences, 1,(1 & 2), 1991, 1-4, (with D. P. Jacobs and Frank Harary) (refereed).

52. Fast Change of Basis in Algebras, Applicable Algebra in Engineering, Communication, and Computing, 3 (1992), 257-261, (with D. P. Jacobs).

53. A Condition Guaranteeing Commutativity, International Journal of Algebra and Computation, Vol. 2, No. 3, (1992), 291-295, (with D. P. Jacobs).

54. Experimenting with the Identity (xy)z = y(zx), Journal of Symbolic Computation, 16 (1993), 289- 293. (with D. P. Jacobs and S. V. Muddana).

55. The Identities of the Simple Non-special Jordan Algebra, accepted modulo revisions by Communications in Algebra (Summer 1993).

56. Solvability of the Ideal of All Weight Zero Elements in Bernstein Algebras, Communications in Algebra  22 (9) (1994), 3264-3275 (with D. P. Jacobs, L. A. Peresi, and S. R. Sverchkov). 

57. Minimal Identities of Berstein Algebras, Algebras, Groups, and Geometries, Volume 11, No. 2, June 1994, (with I. Correa and L. A. Peresi).

58. Rings with (a, b, c) = (a, c, b) and (a, [b, c], d) = 0A Case Study Using Albert, Intern. J. Computer Math 49 (1993), 19-27, (with D. P. Jacobs and Erwin Kleinfeld).

59. Rings with (R,R,R) and [R,(R,R,R)] in the Left Nucleus, Tamkang J.Math., 27 (1996), 183-187, (with C. T. Yen).

60. Degree Three, Four and Five Identities of Quadratic Algebras. Accepted by J. Algebra, Summer 1997 (with L. A. Peresi).

61. Identities of Cayley Dickson Algebras, J. Algebra 188 (1997), 292-306, (with L. A. Peresi).

62. Commutative Center = Center in a Prime Finitely Generated Right Alternative Ring, (with H. F. Smith and E. Kleinfeld), accepted by J. Algebra, January 1997.

63. The Ideal Generated by Sets Contained in the Nuclei, Soochow Journal of Mathematics, 22 (1996), 435-438, (with Chen-te Yen).

64. A Basis for Free Assosymmetric Algebras, J. of Algebra, 183 (1996), 306-318, (with D. P.Jacobs and L. A. Peresi).

65. The McCrimmon Radical for Identities of Degree 3, Sigsam Bulletin, Vol 31, No. 1, Issue 119, pp. 2-5 (1997) (with S. Bondari).

66. On Matrix Structures Invariant under Toda-Like Isospectral Flows, Lin. Alg. & Appl., 254:29- 48 (1997) (with K. Driessel & D. Ashlock).

67. On Matrix Structures Invariant under Toda-Like Isospectral Flows: Sign-Scaled Algebras, submitted to Linear Algebra & Applications, Fall 1997, (with K. Driessel and D. Ashlock).

68. Cantor Ternary Set and Measurability of Hamel Bases, Far East Journal of Mathematical Sciences, Vol. 6, No. 1, (1998), (with A. Abian). 

69. On Computing Eigenvalues and Double Bracket Algebras (with K. R. Driessel), accepted by Hyadronic Journal.

70. Solving AX=B for X with the Most Zeros, accepted by Atas of the Escola de Algebra, January 1999.

71. The Commuting Nucleus of Right Alternative Rings, accepted by Proceedings of the IV
International Conference on Non- Associative Algebra and its Applications, January 1999.

72. Generalized Quadratic Algebras, submitted to Journal of Algebra, July 1998 (with Luiz Peresi).

73. On preserving structured matrices using Double Bracket Operators: Tridiagonal and Toeplitz Matrices (with K. R. Driessel and W. So), preprint stage.

74. On the Dynamics of Ski Skating, (with K. R. Driessel and P. Fink), preprint stage. 


1. HOW TO WIN AT MONOPOLY, Saturday Review of the Sciences, April (1973), 44-48.

2. TRIANGULAR PUZZLE PEG, J. Rec. Math. 6 (1973), 280-283.

3. COMPUTERS IN NON-ASSOCIATIVE RINGS AND ALGEBRAS, ed. by R. Beck and B. Kolman (1977), reviewed August, 1978.

4. TIC-TAC-TOTAL, 4-Star Puzzler 28 (1983), 12, (with Ron Smith).

5. TRIANGULAR PUZZLE PEG, J. Rec. Math., 18 (4) (1985-86), 253-256 (with R. R. Hentzel).

6. Problem accepted by Mathematics Magazine, Dec. 1991. The construction of a point a,b,c units from the corners of a square.

7. AKPATOK ISLAND REVISITED, Environmental Conservation, 19, No. 4, Winter 1992.

8. RETURN TO AKPATOK ISLAND, Environmental Awareness, Vol. 20, No. 2, 65-71 (1997).

9. THE MATH PROFESSOR’S SECRETS OF WINNING AT MONOPOLY EVERY TIME, Bottom Line Personal, October 15, 1997. Interviewed by Any Feinberg.