A new characterization of commutative Artinian rings
Commutative Algebra
2007-05-23 v1
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}].
Cite
@article{arxiv.math/0407270,
title = {A new characterization of commutative Artinian rings},
author = {Kamran Divaani-Aazar and Amir Mafi},
journal= {arXiv preprint arXiv:math/0407270},
year = {2007}
}
Comments
5 pages. Accepted for publications in Vietnam Journal of Mathematics