On P-Essential Submodules

  • 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
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.

Published
2021-12-30
How to Cite
Shahad, H. A., & Al-Mothafar, N. S. (2021). On P-Essential Submodules. Iraqi Journal of Science, 62(12), 4916-4922. https://doi.org/10.24996/ijs.2021.62.12.29
Section
Mathematics