International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 41-46

Primary decomposition of torsion R[X]-modules

William A. Adkins

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 R[X]-modules M which are torsion free as R-modules. Specifically, if an R[X]-submodule of M is pure as an R-submodule, then the primary decomposition of M 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.