Envelopes of commutative rings

Details Envelopes of commutative rings Envelopes of commutative rings

2009-06-23

arxiv.org/abs/0906.4357v1

Mathematics

Commutative Algebra

28 pages, 1 figure

Scientific paper

Given a significative class $F$ of commutative rings, we study the precise conditions under which a commutative ring $R$ has an $F$-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.

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