Two-sided essential nilpotence

Two-sided essential nilpotence

An ideal I of a ring A is essentially nilpotent if I contains a nilpotent ideal N of A such that J⋂N≠0 whenever J is a nonzero ideal of A contained in I. We show that each ring A has a unique largest essentially nilpotent ideal EN(A). We study the properties of EN(A) and, in particular, we investiga...

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Bibliographic Details
Main Authors: Esfandiar Eslami, Patrick Stewart
Format: Article
Language:English
Published: Hindawi Limited 1992-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
essential ideal
nilpotent ideal
free normalizing extension
crossed product
Morita equivalent
fixed ring.
Online Access:http://dx.doi.org/10.1155/S0161171292000449
Description
Summary:An ideal I of a ring A is essentially nilpotent if I contains a nilpotent ideal N of A such that J⋂N≠0 whenever J is a nonzero ideal of A contained in I. We show that each ring A has a unique largest essentially nilpotent ideal EN(A). We study the properties of EN(A) and, in particular, we investigate how this ideal behaves with respect to related rings.
ISSN:0161-1712
1687-0425

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