| 基于环的左理想半群生成的凯莱图 |
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| 作者姓名： | Aihua Li Ralph P.Tucci |
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| 作者单位： | Department of Mathematical Sciences,Montclair State University;Department of Mathematical Sciences,Loyola University New Orleans |
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| 摘 要： | We investigate the interaction between a ring R and the Cayley graph Cay（L（R）） of the semigroup of left ideals of R,as well as subdigraphs of this graph. Graph theoretic properties of these graphs are investigated,such as transitive closure,girth,radius,diameter,and spanning subgraphs.Conditions on certain of these graphs are given which imply that R is regular,left duo,or that the idempotents of R are central. We characterize simple rings in terms of Cay（L（R））. We characterize strongly regular rings in terms of a subdigraph of Cay（L（R））.
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| 关 键 词： | Cayley graph semigroup left ideal |
| 收稿时间： | 2014/7/20 0:00:00 |
The Cayley graph built upon the semigroup of left ideals of a ring |
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| Aihua Li,Ralph P.Tucci.The Cayley graph built upon the semigroup of left ideals of a ring[J].Journal of Shanghai Normal University(Natural Sciences),2014,43(5):506-510. |
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| Authors: | Aihua Li Ralph PTucci |
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| Abstract: | We investigate the interaction between a ring R and the Cayley graph Cay(L(R)) of the semigroup of left ideals of R,as well as subdigraphs of this graph. Graph theoretic properties of these graphs are investigated,such as transitive closure,girth,radius,diameter,and spanning subgraphs.Conditions on certain of these graphs are given which imply that R is regular,left duo,or that the idempotents of R are central. We characterize simple rings in terms of Cay(L(R)). We characterize strongly regular rings in terms of a subdigraph of Cay(L(R)). |
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| Keywords: | Cayley graph semigroup left ideal |
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