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Envelopes of Commutative Rings
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作者 Rafael PARRA manuel saorin 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第3期561-580,共20页
Given a significative class F of commutative rings, we study the precise conditions under which a commutative ring R has an S-envelope. A full answer is obtained when F is the class of fields, semisimple commutative r... Given a significative class F of commutative rings, we study the precise conditions under which a commutative ring R has an S-envelope. A full answer is obtained when F is the class of fields, semisimple commutative rings or integral domains. When .F is the class of Noetherian rings, we give a full answer when the Krull dimension of R is zero and when the envelope is required to be epimorphic. The general problem is reduced to identifying the class of non-Noetherian rings having a monomorphic Noetherian envelope, which we conjecture is the empty class. 展开更多
关键词 Noetherian ring ENVELOPE local ring artinian ring Krull dimension
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