WEAKLY IRREDUCIBLE IDEALS

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.