Properties of a certain product of submodules - Heidari, S.; Nikandish, R.; Nikmehr, M. J. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
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.