Almost prime ideals in noncommutative rings

2022/01/24 by Abouhalaka, Alaa, Findik, Sehmus
#13A15 #17A01 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2201.09758

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.

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