paper

A new characterization of commutative Artinian rings

arXiv:math/0407270

Abstract

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

5 pages. Accepted for publications in Vietnam Journal of Mathematics

A new characterization of commutative Artinian rings · wovepaper