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- W2108779901 abstract "E. Matlis proved that if R is an integral domain with quotient field Q and K is the R-module Q/R, then all torsion R-modules decompose into a direct sum of local submodules if and only if K decomposes into a direct sum of local submodules. Thus K is a test module to determine whether torsion modules decompose. We generalize this result to commutative rings. If R is a commutative ring and a torsion theory of R is given by a Gabriel topology , then form the ring of quotients R and let K be the cokernel of the canonical ring homomorphism from R to R. In some special cases, every -torsion R-module decomposes into a direct sum of local submodules if and only if K decomposes. However, there is an example where this is not the case. The principal result is: given R, and K, there is a related filter K of ideals of R, which is a subset of , such that all K-pretorsion R-modules decompose into a direct sum of local submodules if and only if K decomposes. The relationship between and K is investigated." @default.
- W2108779901 created "2016-06-24" @default.
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- W2108779901 date "1987-01-01" @default.
- W2108779901 modified "2023-09-23" @default.
- W2108779901 title "Decomposing torsion modules" @default.
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- W2108779901 doi "https://doi.org/10.1080/00927878708823459" @default.
- W2108779901 hasPublicationYear "1987" @default.
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