A new characterization of commutative Artinian rings

Details A new characterization of commutative Artinian rings A new characterization of commutative Artinian rings

2004-07-15

arxiv.org/abs/math/0407270v1

Mathematics

Commutative Algebra

5 pages. Accepted for publications in Vietnam Journal of Mathematics

Scientific paper

Let $R$ be a commutative Noetherian ring. It is shown that $R$ is Artinian if
and only if every $R$-module is good, if and only if every $R$-module is
representable. As a result, it follows that every nonzero submodule of any
representable $R$-module is representable if and only if $R$ is Artinian. This
provides an answer to a question which is investigated in [{\bf 1}].

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