Modules Satisfying the Ascending Chain Condition on Submodules with Bounded Uniform Dimension

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

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
• 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