|
|
Two-sided essential nilpotenceDOI: 10.1155/s0161171292000449 Keywords: essential ideal , nilpotent ideal , free normalizing extension , crossed product , Morita equivalent , fixed ring. 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.
|
