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Finite completely primary rings in which the product of any two zero divisors of a ring is in its coefficient subring

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  • Yousif Alkhamees

Abstract

According to general terminology, a ring R is completely primary if its set of zero divisors J forms an ideal. Let R be a finite completely primary ring. It is easy to establish that J is the unique maximal ideal of R and R has a coefficient subring S (i.e. R / J isomorphic to S / p S ) which is a Galois ring. In this paper we give the construction of finite completely primary rings in which the product of any two zero divisors is in S and determine their enumeration. We also show that finite rings in which the product of any two zero divisors is a power of a fixed prime p are completely primary rings with either J 2 = 0 or their coefficient subring is Z 2 n with n = 2 or 3 . A special case of these rings is the class of finite rings, studied in [2], in which the product of any two zero divisors is zero.

Suggested Citation

  • Yousif Alkhamees, 1994. "Finite completely primary rings in which the product of any two zero divisors of a ring is in its coefficient subring," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:682979
    DOI: 10.1155/S0161171294000670
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