Open AccessOn P-Essential Submodules
Author(s) -
Haithab A. Shahad,
Nuhad S. Al-Mothafar
Publication year - 2021
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2021.62.12.29
Subject(s) - commutative ring , mathematics , multiplication (music) , identity (music) , prime (order theory) , commutative property , pure mathematics , zero (linguistics) , ring (chemistry) , discrete mathematics , combinatorics , physics , chemistry , linguistics , philosophy , organic chemistry , acoustics
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.