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 diagonalizablc linear transformation of any invariant subspace. Additionally, primary decompositions are considered under direct sums and tensor product. © 1994, Hindawi Publishing Corporation. All rights reserved.
Publication Source (Journal or Book title)
International Journal of Mathematics and Mathematical Sciences
Adkins, W. (1994). Primary Decomposition of Torsion R[X]-Modules. International Journal of Mathematics and Mathematical Sciences, 17 (1), 41-46. https://doi.org/10.1155/S0161171294000074