Campos, E.S. and Smith, P.F. (2009) Modules Satisfying the Ascending Chain Condition on Submodules with Bounded Uniform Dimension. In: Dung, N.V., Guerriero, F., Hammoudi, L. and Kanwar, P. (eds.) Rings, Modules and Representations. Series: Contemporary Mathematics Series (480). American Mathematical Society: Providence, RI, pp. 57-71. ISBN 978-0-8218-4370-3
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Abstract
We say that a module M satisfies pand-acc provided every submodule with finite uniform dimension is Noetherian. We investigate rings for which every module satisfies pand-acc and characterize the commutative rings with this property. It is proved that if R is a right Noetherian ring which is either right nonsingular or left Noetherian then every torsionless right R-module satisfies pand-acc. However, in general a direct product of simple modules need not satisfy pand-acc.
Item Type: | Book Sections |
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Additional Information: | International Conference on Rings and Things held in Honor of Carl Faith and Barbara Osofsky, Ohio Univ, Zanesville, Zanesville, OH, JUN 15-17, 2007 Series ISSN: 0271-4132 |
Status: | Published |
Glasgow Author(s) Enlighten ID: | Smith, Professor Patrick |
Authors: | Campos, E.S., and Smith, P.F. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Publisher: | American Mathematical Society |
ISBN: | 978-0-8218-4370-3 |
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