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On the Matlis reflexive modules
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DOI：10.32513/asetmj/193220082619107.png)
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Abstract
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Let (R, m) denote a complete local ring and let M be a Matlis reflexive R-module of positive dimension. The purpose of this article is to show that for every minimal element p of AssR(M), the Rp-module Mp has finite length. As a consequence, we provide a new proof of Enochs' Theorem, i.e., M is Matlis reflexive if and only if it has a finitely generated submodule N such that M/N is Artinian.
Keywords:
associated primes
complete ring
Mathis reflexive
minimax module
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