Exchange Ideals with All Idempotents Central

Abstract

In this paper we investigate necessary and sufficient conditions on an ideal under which it is an exchange ideal with all idempotents central. Related examples are constructed by means of ideal-extensions. A kind of uniqueness in such ideals is also studied. These provide a new class of such ideals.

Semicommutativity of the rings relative to prime radical

“…These rings are extensively studied by many authors, namely, [1], [3], [4], [5] and [15]. Nicholson proved that every clean ring is exchange.…”