Unique irredundant intersections of completely irreducible ideals
نویسندگان
چکیده
منابع مشابه
Commutative Ideal Theory without Finiteness Conditions: Completely Irreducible Ideals
An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an ir...
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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 bee...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2005
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.03.001