International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 41-46
Primary decomposition of torsion -modules
Department of Mathematics, Louisiana State University, Baton Rouge 70803, Louisiana, USA
Received 22 September 1992; Revised 18 March 1993
Copyright © 1994 William A. Adkins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper is concerned with studying hereditary properties of primary decompositions of torsion -modules which are torsion free as -modules. Specifically, if an -submodule of is pure as an -submodule, then the primary decomposition of determines a primary decomposition of the submodule. This is a generalization of the classical fact from linear algebra that a diagonalizable linear transformation on a vector space restricts to a diagonalizable linear transformation of any invariant subspace. Additionally, primary decompositions are considered under direct sums and tensor product.