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Classification of rings with toroidal annihilating-ideal graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 3، شماره 2، زمستان 2018، صفحه 93-119 اصل مقاله (328.95 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2018.26060.1072 | ||
| نویسندگان | ||
Selvakumar Krishnan  1؛ Subbulakshmi P2
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| 1Department of Mathematics Manonmaniam Sundaranar University Tirunelveli | ||
| 2Manonmaniam Sundaranar University | ||
| چکیده | ||
| Let R be a non-domain commutative ring with identity and A(R) be the set of non-zero ideals with non-zero annihilators. We call an ideal I of R, an annihilating-ideal if there exists a non-zero ideal J of R such that IJ = (0). The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R) and two distinct vertices I and J are adjacent if and only if IJ = (0). In this paper, we characterize all commutative Artinian nonlocal rings R for which AG(R) has genus one. | ||
| کلیدواژهها | ||
| annihilating-ideal؛ planar؛ genus؛ local ring؛ annihilating-ideal graph | ||
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آمار تعداد مشاهده مقاله: 588 تعداد دریافت فایل اصل مقاله: 430 |
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