- 期刊
PRIMARY DECOMPOSITION OF TORSION R[X]-MODULES
摘要
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 am 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.
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