Two-sided essential nilpotence

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.

Keywords

• essential ideal
• nilpotent ideal
• free normalizing extension
• crossed product
• Morita equivalent
• fixed ring.