University of Guilan Journal of Algebra and Related Topics 2345-3931 3 1 2015 06 01 A note on maximal non-prime ideals 51 61 1213 EN S. Visweswaran Saurashtra University A. Parmar Saurashtra University Journal Article 2015 06 12 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 $R$. https://jart.guilan.ac.ir/article_1213_ef7c4b9f1125da4eb7d276b1d9cbcb6d.pdf