%0 Journal Article
%T A note on maximal non-prime ideals
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Visweswaran, S.
%A Parmar, A.
%D 2015
%\ 06/01/2015
%V 3
%N 1
%P 51-61
%! A note on maximal non-prime ideals
%K Maximal non-prime ideal
%K maximal non-maximal ideal
%K maximal non-primary ideal
%K maximal non-irreducible ideal
%R
%X The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$, we mean an ideal $I$ of $R$ such that $Ineq R$. 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 $ Isubseteq A$ and $Ineq A$ 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 $R$.
%U https://jart.guilan.ac.ir/article_1213_ef7c4b9f1125da4eb7d276b1d9cbcb6d.pdf