Primary decomposition of torsion R [ X ] -modules

William A. Adkins

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-6

Abstract:

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.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:456270

DOI: 10.1155/S0161171294000074

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