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Classification of rings with toroidal annihilating-ideal graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 3، شماره 2، اسفند 2018، صفحه 93-119 اصل مقاله (328.92 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2018.26060.1072 | ||
| نویسندگان | ||
| Selvakumar Krishnan* 1؛ Subbulakshmi P2 | ||
| 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 | ||
| مراجع | ||
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