JP Journal of Algebra, Number Theory and Applications
Volume 10, Issue 1, Pages 65 - 79
(February 2008)
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C-PRIMARY DECOMPOSITION FOR MODULES
Jaime Castro P鲥z (M鸩co)
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Abstract: This paper is concerned with the study of the
-primary decomposition for a module on a ring R. We use the concept of
-module, studied in [1] and [2], to define
-coprimary and
-primary modules, where
is a subset of
see [1, Definition 1.5]. Given a proper submodule N of an R-module M, we define the -primary decomposition of N in M. The -primary decomposition is a generalization of the primary decomposition given by Goldman in [6]. We prove that an R-module M is a -module if and only if for each proper submodule N of M, N has -primary decomposition in M. Examples are given to illustrate the theory. |
Keywords and phrases: torsion theory, primary decomposition, lattice. |
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