On P-Essential Submodules

Haithab A.  Shahad; Nuhad Salim  Al-Mothafar

doi:10.24996/ijs.2021.62.12.29

Authors

Haithab A. Shahad Department of Mathematics, College of Education for Science, University of Baghdad
Nuhad Salim Al-Mothafar Department of Mathematics, College of Education for Science, University of Baghdad

DOI:

https://doi.org/10.24996/ijs.2021.62.12.29

Keywords:

Essential submodules, Uniform modules, Fully prime modules, multiplications modules

Abstract

Let be a commutative ring with identity and let be an R-module. We call an R-submodule of as P-essential if for each nonzero prime submodule of and 0 . Also, we call an R-module as P-uniform if every non-zero submodule of is P-essential. We give some properties of P-essential and introduce many properties to P-uniform R-module. Also, we give conditions under which a submodule of a multiplication R-module becomes P-essential. Moreover, various properties of P-essential submodules are considered.