PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS
عنوان مقاله: PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS
شناسه ملی مقاله: JR_JAS-10-2_010
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_JAS-10-2_010
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
M. Adlifard - Department of Mathematics, Roudbar Branch, Islamic Azad University, Roudbar, Iran.
Sh. Payrovi - Department of Mathematics, Imam Khomeini International University, P.O. Box ۳۴۱۴۹-۱-۶۸۱۸, Qazvin, Iran.
خلاصه مقاله:
M. Adlifard - Department of Mathematics, Roudbar Branch, Islamic Azad University, Roudbar, Iran.
Sh. Payrovi - Department of Mathematics, Imam Khomeini International University, P.O. Box ۳۴۱۴۹-۱-۶۸۱۸, Qazvin, Iran.
Let R be a commutative ring and Z(R) be the set of its zero-divisors.The annihilator graph of R, denoted by AG(R) is a simple undirected graph whose vertexset is Z(R)^*, the set of all nonzero zero-divisors of R, and two distinct vertices x andy are adjacent if and only if {\rm ann}_R(xy)\neq {\rm ann}_R(x)\cup {\rm ann}_R(y).In this paper, perfectness of the annihilator graph for some classes of rings is investigated.More precisely, we show that if R is an Artinian ring, then AG(R) is perfect.
کلمات کلیدی: Artinian ring, Annihilator graph, Perfectness
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1489984/