P-Essential Maximal Submodules

Ahmed K.  Mawlood; Nuhad S.  Al-Mothafar

doi:10.30526/39.4.4357

Authors

Ahmed K. Mawlood Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0009-0004-9028-3661
Nuhad S. Al-Mothafar Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0003-2392-3927

DOI:

https://doi.org/10.30526/39.4.4357

Keywords:

maximal submodules, P-essential maximal submodules, P-essential local, P-essential radical.

Abstract

Let be a commutative ring with identity and be a unitary left -module. The main goal of this work is to introduce and study the idea of a P-essential maximal submodule, which is a generalization for maximal submodules, as a proper submodule of an -Mod is called P-essential maximal (shortly Pe-max) if for any P-essential submodule of a module with implies that , where a sub mod of an -Mod is called P-essential in , if such that , implies . An ideal of a ring is called P-essential maximal ideal, if for any Pe-ideal of such that implies . And we introduce the concept P-essential local, an -Mod is called P-essential local module (for short Pe-local), if it has only one Pe-maximal submodule, which is contains each proper submodule of . And we research some relationships between P-essential maximal submodules and some other related ideas. Moreover, we give P-essential local module and P-essential radical module. Some properties and many results were proved as well as the behaviour of that concept with its localization was studied and shown

Author Biographies

Ahmed K. Mawlood, Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

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Nuhad S. Al-Mothafar , Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

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