GENERALIZED QUASI-PRIMARY RINGS
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In this paper, the structure of commutative rings with identity all of whose ideals are quasi-primary, called generalized quasi-primary rings, is studied and several equivalent conditions to such rings are considered. Equivalently, a generalized quasi-primary ring may be viewed as a ring whose the set of radical ideals forms a chain. It is proved that an Artinian local ring R is a generalized quasi-primary ring and the converse is true if R is a non-domain Noetherian ring.
Abstract
In this paper, the structure of commutative rings with identity all of whose ideals are quasi-primary, called generalized quasi-primary rings, is studied and several equivalent conditions to such rings are considered. Equivalently, a generalized quasi-primary ring may be viewed as a ring whose the set of radical ideals forms a chain. It is proved that an Artinian local ring R is a generalized quasi-primary ring and the converse is true if R is a non-domain Noetherian ring.
참고문헌 (9)
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