Volume no :1, Issue no: 1, March (2008)

Journal of Algebra, Number Theory: Advances and Applications

STRONG ZERO DIVISORS

Author's: Abraham A. Klein
Pages: [29] - [36]
Received Date: November 13, 2008
Submitted by:

Abstract

A subset of an infinite ring R is said to be large, if it has the same cardinality as R, and small otherwise. For R which is not a domain, we study the set of all zero divisors with large two-sided annihilator. We show that contains all small ideals and the set of all nilpotents and if is small, contains the ideal generated by If is small, it is an ideal containing all small one-sided ideals. The structure of rings with finite is given.

Keywords

strong zero divisors, two-sided annihilator, prime radical, semiprime ring.