International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 351-354
doi:10.1155/S0161171292000449
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
Abstract
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.