Properties of a certain product of submodules

Authors

  • S. Heidari K. N. Toosi Univ. Technology, Iran
  • R. Nikandish K. N. Toosi Univ. Technology, Iran
  • M. J. Nikmehr K. N. Toosi Univ. Technology, Iran

Abstract

Let R be a commutative ring with identity, M an R-module and K1,...,Kn submodules of M. In this article, we construct an algebraic object, called product of K1,...,Kn. We equipped this structure with appropriate operations to get an R(M)-module. It is shown that R(M)-module Mn=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 Mn is a projective (flat) R(M)-module.

Published

25.04.2011

Issue

Section

Research articles

How to Cite

Heidari, S., et al. “Properties of a Certain Product of Submodules”. Ukrains’kyi Matematychnyi Zhurnal, vol. 63, no. 4, Apr. 2011, pp. 502-1, https://umj.imath.kiev.ua/index.php/umj/article/view/2736.