Volume 13, Issue 1 (5-2018)                   IJMSI 2018, 13(1): 67-73 | Back to browse issues page

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Let $R$ be a commutative ring and $I$ an ideal of $R$. The zero-divisor graph of $R$ with respect to $I$, denoted by $Gamma_I(R)$, is the simple graph whose vertex set is ${x in Rsetminus I mid xy in I$, for some $y in Rsetminus I}$, with two distinct vertices $x$ and $y$ are adjacent if and only if $xy in I$. In this paper, we state a relation between zero-divisor graph of $R$ with respect to an ideal and almost prime ideals of $R$. We then use this result to give a graphical characterization for $SPAP$-rings.

Type of Study: Research paper | Subject: Special