Almost prime ideals in noncommutative rings

Abstract

A proper ideal $P$ of a commutative ring with identity is an almost prime ideal if $ab\in P\setminus P^2$ implies $a\in P$ or $b\in P$. In this paper we define almost prime ideals of a noncommutative ring, and provide some equivalent definitions. We also examine some cases such that all right ideals of a noncommutative ring are almost prime right ideals.

9 Pages