2018
Том 70
№ 9

# Properties of a certain product of submodules

Abstract

Let $R$ be a commutative ring with identity, $M$ an $R$-module and $K_1,..., K_n$ submodules of $M$. In this article, we construct an algebraic object, called product of $K_1,..., K_n$. We equipped this structure with appropriate operations to get an $R(M)$-module. It is shown that $R(M)$-module $M^n = M... M$ and $R$-module $M$ inherit some of the most important properties of each other. For example, we show that $M$ is a projective (flat) $R$-module if and only if $M^n$ is a projective (flat) $R(M)$-module.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 4, pp 580-595.

Citation Example: Heidari S., Nikandish R., Nikmehr M. J. Properties of a certain product of submodules // Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 502-512.

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