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A survey on the Intersection graphs of ideals of rings | ||
Communications in Combinatorics and Optimization | ||
مقاله 13، دوره 7، شماره 2، اسفند 2022، صفحه 121-167 اصل مقاله (656.7 K) | ||
نوع مقاله: Survey paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2021.26990.1176 | ||
نویسندگان | ||
Ivy Chakrabarty1؛ Joseph Varghese Kureethara* 2 | ||
1Independent Researcher | ||
2Christ University | ||
چکیده | ||
Let L(R) denote the set of all non-trivial left ideals of a ring R. The intersection graph of ideals of a ring R is an undirected simple graph denoted by G(R) whose vertices are in a one-to-one correspondence with L(R) and two distinct vertices are joined by an edge if and only if the corresponding left ideals of R have a non-zero intersection. The ideal structure of a ring reflects many ring theoretical properties. Thus much research has been conducted last few years to explore the properties of G(R). This is a survey of the developments in the study on the intersection graphs of ideals of rings since its introduction in 2009. | ||
کلیدواژهها | ||
Ring؛ Artinian ring؛ ideal of a ring؛ intersection graph؛ Algebraic Graph Theory | ||
مراجع | ||
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