ALMOST PRIME IDEALS IN NONCOMMUTATIVE RINGS

Abstract

A proper ideal P of a commutative ring with identity is an almost prime ideal if ab ∈ P\P2 implies a ∈ P or b ∈ 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.