Strongly Hollow R - Annihilator Lifting Modules and Strongly R - Annihilator (Hollow- Lifting) Modules

  • Omar K. Ibrahim Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • Alaa A. Elewi Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: R-annihilator submodule, coessential submodule, hollow-lifting module, strongly hollow lifting module

Abstract

Let R be a commutative ring with unity. Let W be an R-module, for K≤F, where F is a submodule of W and K is said to be R-annihilator coessential submodule of F in W (briefly R-a-coessential) if  (denoted by K  F in W). An R-module W is called strongly hollow -R-annihilator -lifting module (briefly, strongly hollow-R-a-lifting), if for every submodule F of W with  hollow, there exists a fully invariant direct summand K of W such that K  F in W. An R - module W is called strongly R - annihilator - ( hollow - lifting ) module ( briefly strongly R - a - ( hollow - lifting ) module ), if for every submodule F of W with   R - a - hollow, there exists a fully invariant direct summand K of W such that K  F in W.

Published
2020-11-28
How to Cite
Ibrahim, O. K., & Elewi, A. A. (2020). Strongly Hollow R - Annihilator Lifting Modules and Strongly R - Annihilator (Hollow- Lifting) Modules. Iraqi Journal of Science, 61(11), 3047-3052. https://doi.org/10.24996/ijs.2020.61.11.25
Section
Mathematics