International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 351-354
Two-sided essential nilpotence
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 of a ring is essentially nilpotent if contains a nilpotent ideal of such that whenever is a nonzero ideal of contained in . We show that each ring has a unique largest essentially nilpotent ideal . We study the properties of and, in particular, we investigate how this ideal behaves with respect to related rings.