Max-fully cancellation modules

Dr. Bothaynah Nijad Shihab; Heba Mohammad Ali Judi

doi:10.24297/jam.v11i7.1225

Authors

Dr. Bothaynah Nijad Shihab College of Education for pure Science /Ibn-AL-Haitham, University of Baghdad , Baghdad,
Heba Mohammad Ali Judi College of Education for pure Science /Ibn-AL-Haitham, University of Baghdad , Baghdad,

DOI:

https://doi.org/10.24297/jam.v11i7.1225

Abstract

Let R be a commutative ring with identity and let M be a unital an R`-module. We introduce the concept of max-fully cancellation R-module , where an R-module M is called max-fully cancellation if for every nonzero maximal ideal I of R and every two submodules N₁And N₂, of M such that IN₁ =IN₂ , implies = N₁ and N₂ . some characterization of this concept is given and some properties of this concept are proved. The direct sum and the trace of module with max-fully cancellation modules are studied , also the localization of max-fully cancellation module are discussed..