Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 1, pp. 61-74 (2004)
Pure submodules of multiplication modules
Majid M. Ali and David J. SmithDepartment of Mathematics, Sultan Qaboos University, Muscat, Oman, e-mail: firstname.lastname@example.org; Department of Mathematics, University of Auckland, Auckland, New Zealand, e-mail: email@example.com
Abstract: The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are considered. We also give two descriptions for the trace of a pure submodule of a multiplication module.
Keywords: multiplication module, pure submodule, idempotent submodule, flat module, projective module, radical of a module, trace of a module
Classification (MSC2000): 13C13, 13C05, 13A15
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Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.