Weakly irreducible ideals

Document Type: Research Paper


1 Department of Mathematics, Velayat University, Iranshahr, Iran.

2 Department of Mathematics, University of Birjand, Birjand, Iran.


Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has been given. Also the relations between weakly irreducible ideals of $R$ and weakly irreducible ideals of localizations of the ring $R$ are also studied.