P-ideals and PMP-ideals in Commutative rings

Authors

  • Jamal Hashemi zadeh Dezfuly Shahid Chamran University of Ahvaz
  • Ali Rezaei Aliabad Shahid Chamran University of Ahvaz
  • Rostam Mohamadian Shahid Chamran University of Ahvaz

DOI:

https://doi.org/10.30495/jme.v10i0.422

Keywords:

P-ideal, PMP-ideal, pure ideal, von Neumann regular ideal, P-space.

Abstract

Recently,  P-ideals  studied in ${\rm C}(X)$ by some authors. In this article we investigate {\rm P}-ideals and a new concept as PMP-ideals in commutative rings. We show that $I$ is a {\rm P}-ideal (resp.,
{\rm PMP}-ideal) in $R$ if and only if every prime ideal of $R$ which
does not contain $I$ is a maximal (resp., minimal prime) ideal of
$R$. Also, we characterize largest {\rm P}-ideals (resp., PMP-ideals) in commutative rings, specially in ${\rm C}(X)$. Furthermore, we study relation between these ideals and pure ideals.
%\end{abstract}
Finally we prove that ${\rm C}(X)$ is a von Neumann regular ring if and only if every   pure ideal of it is P-ideal.

Author Biographies

Jamal Hashemi zadeh Dezfuly, Shahid Chamran University of Ahvaz

Mathematics department

Ali Rezaei Aliabad, Shahid Chamran University of Ahvaz

Mathematics department

Rostam Mohamadian, Shahid Chamran University of Ahvaz

Mathematics department

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Published

2016-10-12

Issue

Section

Vol. 10, No. 4, (2016)