A classification of cube radical zero completely primary finite rings

• Autorzy: Chikunji Ch. J.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider the isomorphism problem of a class of completely primary finite rings R such that if M. is the Jacobson radical of R, thenM3 = (0) and M2 = (0), in the general case (not necessarily the case where the maximal Galois subrings lie in the center). We further obtain the number of non-isomorphic classes in a special case of these rings.

Słowa kluczowe

EN

isomorphism; Jacobson radical; primary finite rings

PL

izomorfizm; pierścienie skończone; pierwiastek Jacobsona

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 7--20
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Chikunji Ch. J.

• Department of Mathematics, University of Transkei, P/Bag X1, Umtata 5117, Republic of South Africa

Bibliografia

• [1] C. J. Chikunji, On a class of finite rings, Comm. Algebra, 27 (1999), 5049-5081.
• [2] C. J. Chikunji, Using MATLAB to solve a classification problem in finite rings, Proc. ICM2, Univ. Crete, 1-6 July, 2002, Crete, Greece, pp. 252.
• [3] C. J. Chikunji, Enumeration of finite rings with Jacobson radical of cube zero, (in press with SAMSA Journal).
• [4] W. E. Clark, A coefficient ring for finite non-commutative rings, Proc. Amer. Math. Soc. 33 (1972), 25-28.
• [5] B. Corbas, Rings with few zero divisors, Math. Ann. 181 (1969), 1-7.
• [6] R. Raghavendran, Finite associative rings, Compositio Math. 21, Fasc. 2 (1969), 195-229.
• [7] B. R. Wirt, Finite non-commutative local rings, Ph.D. Thesis, University of Oklahoma (1972).