Some remarks on multiplication ideals,ii |
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Authors: | D.D. Anderson |
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Affiliation: | Department of mathematics , The university of Iowa , Iowa City, IA, 52242, U.S.A |
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Abstract: | Let R bea commutative ring with identity. An R-module (ideal of R) A is called a multiplication module (ideal) if for each submodule N of A there exists an ideal I of R with N = I A. We give several characterizations of multiplication modules. Using the method of idealization we show how to reduce questions concerning multiplication modules to multiplication ideals. For example, we show that if S is a commutative R-algebra and ψ: M→an R-module homomorphism where M is a multiplication R-module and N is an S-module, then Sψ(M) is a multiplication S-module. |
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