International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 351-354

Two-sided essential nilpotence

Esfandiar Eslami1 and Patrick Stewart2

1Department of Mathematics, University of Kerman, Kerman, Iran
2Department of Mathematics, Dalhousie University, Nova Scotia, Halifax B3H 3J5, Canada

Received 25 January 1991

Copyright © 1992 Esfandiar Eslami and Patrick Stewart. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An ideal I of a ring A is essentially nilpotent if I contains a nilpotent ideal N of A such that JN0 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.