Homogeneous idealization and some dual notions around comultiplication modules

Jalal Abadi, Batool Zarei and Moghimi, Hosein Fazaeli (2017) Homogeneous idealization and some dual notions around comultiplication modules. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 33 (2). pp. 175-185. ISSN 0866-0174

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Abstract

Let R be a commutative ring with identity, and let M be a unital R-module. D. D. Anderson proved that a submodule N of M is multiplication if and only if 0(+)N is a multiplication ideal of R(+)M, the homogeneous idealization of M. In this article, we show that a similar statement holds for comultiplication modules. We develop the tool of idealization of a module particularly in the context of cocyclic modules, self-cogenerator modules, comultiplication modules (self-cogenerated modules), couniform modules, AB5 ∗ modules, direct family and inverse family of submodules.

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