Author:
Gardner B. J.,Stewart P. N.
Abstract
A ring R is prime essential if R is semiprime and for each prime ideal P of R, P ∩ I ≠0 whenever I is a nonzero two-sided ideal of R. Examples of prime essential rings include rings of continuous functions and infinite products modulo infinite sums. We show that the class of prime essential rings is closed under many familiar operations; in particular, we consider polynomial rings, matix rings, fixed rings and skew group rings. Also, we explore the relationship between prime essential rings and special radical classes, and we demonstrate how prime essential rings can be used to construct radical classes which are not special.
Publisher
Cambridge University Press (CUP)
Cited by
9 articles.
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1. A PRIME ESSENTIAL RING THAT GENERATES A SPECIAL ATOM;Bulletin of the Australian Mathematical Society;2016-11-02
2. Some properties of prime essential rings and their generalization;AIP Conference Proceedings;2016
3. ON BAD SUPERNILPOTENT RADICALS;Bulletin of the Australian Mathematical Society;2011-12-15
4. ON SUPERNILPOTENT NONSPECIAL RADICALS;Bulletin of the Australian Mathematical Society;2008-08
5. On generalised prime essential rings and special and nonspecial radicals;Bulletin of the Australian Mathematical Society;2007-10