On P-Essential Submodules

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.

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Published

2021-12-30

Issue

Vol 62 No 12 (2021)

Section

Mathematics

How to Cite

[1]
H. A. . Shahad and N. S. . Al-Mothafar, “On P-Essential Submodules”, Iraqi Journal of Science, vol. 62, no. 12, pp. 4916–4922, Dec. 2021, doi: 10.24996/ijs.2021.62.12.29.
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