@article {
author = {Visweswaran, S. and Parmar, A.},
title = {A note on maximal non-prime ideals},
journal = {Journal of Algebra and Related Topics},
volume = {3},
number = {1},
pages = {51-61},
year = {2015},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {},
abstract = {The rings considered in this article are commutative with identity $1\neq 0$. By a proper ideal of a ring $R$, we mean an ideal $I$ of $R$ such that $I\neq R$. We say that a proper ideal $I$ of a ring $R$ is a maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ I\subseteq A$ and $I\neq A$ is a prime ideal. That is, among all the proper ideals of $R$, $I$ is maximal with respect to the property of being not a prime ideal. The concept of maximal non-maximal ideal and maximal non-primary ideal of a ring can be similarly defined. The aim of this article is to characterize ideals $I$ of a ring $R$ such that $I$ is a maximal non-prime (respectively, a maximal non maximal, a maximal non-primary) ideal of $R$.},
keywords = {Maximal non-prime ideal,maximal non-maximal ideal,maximal non-primary ideal,maximal non-irreducible ideal},
url = {https://jart.guilan.ac.ir/article_1213.html},
eprint = {https://jart.guilan.ac.ir/article_1213_ef7c4b9f1125da4eb7d276b1d9cbcb6d.pdf}
}