A note on near completely prime ideal rings over σ(*)-rings
Abstract
Let $R$ be a ring and $\sigma$ an endomorphism of $R$. Recall that $R$ is said to be a $\sigma(*)$-ring if $a\sigma(a) \in P(R)$ for $a \in R$, where $P(R)$ is the prime radical of $R$. We also recall that a ring $R$ is said to be a completely prime ideal ring (CPI-ring) if every prime ideal of $R$ is completely prime. We say that a ring $R$ is a near completely prime ideal ring (NCPI-ring) if every minimal prime ideal of $R$ is completely prime Bhat [6].
In this paper we give a relation between $\sigma(*)$-ring and near completely prime ideal ring and also proved that if $R$ is a Noetherian ring and $\sigma$ an endomorphism of $R$ such that $R$ is $\sigma(*)$-ring then $S(R) = R[x; \sigma]$ is a Noetherian near completely prime ideal ring.Copyright © 2013 Kiran Chib, V. K. Bhat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
K. Chib, V. K. Bhat, A note on near completely prime ideal rings over σ(*)-rings, J. Math. Comput. Sci. 3 (2013), 1108–1114.
BibTeX
@article{Chib2013,
author = {Chib, Kiran and Bhat, V. K.},
title = {A note on near completely prime ideal rings over σ(*)-rings},
journal = {J. Math. Comput. Sci.},
volume = {3},
year = {2013},
pages = {1108--1114},
doi = {}
}