F-µ-Semiregular Modules

  • Eman Mohammed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • Wasan Khalid Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: µ-small submodule, F-µ-semiregular module

Abstract

Let  R be an associative ring with identity and let M be a left R-module . As a generalization of µ-semiregular modules, we introduce an F-µ-semiregular module. Let F be a submodule of M and x∊M. x is called F-µ-semiregular element in M , if there exists a decomposition M=A⨁B, such that A is a projective submodule of  and . M is called  F-µ-semiregular if x is F-µ-semiregular element for each x∊M. A condition under which the module µ-semiregular is F-µ-semiregular module was given. The basic properties and some characterizations of the F-µ-semiregular module were provided.

Published
2021-04-30
How to Cite
Mohammed, E., & Khalid, W. (2021). F-µ-Semiregular Modules. Iraqi Journal of Science, 62(4), 1271-1275. https://doi.org/10.24996/ijs.2021.62.4.22
Section
Mathematics