Classification of the Toroidal Jacobson Graphs
| Autor: | Mohammad Reza Pournaki, H. Amraei, Hamid Reza Maimani, A. Zaeembashi |
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| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Toroid Noncommutative ring General Mathematics Mathematics::Rings and Algebras 010102 general mathematics 0102 computer and information sciences Jacobson radical Commutative ring 01 natural sciences Graph Vertex (geometry) Combinatorics 010201 computation theory & mathematics Nakayama lemma 0101 mathematics Commutative property Mathematics |
| Zdroj: | Bulletin of the Malaysian Mathematical Sciences Society. 41:321-334 |
| ISSN: | 2180-4206 0126-6705 |
| Popis: | Let R be a finite commutative ring with nonzero identity and denote its Jacobson radical by J(R). The Jacobson graph of R is the graph in which the vertex set is $$R\setminus J(R)$$ , and two distinct vertices x and y are adjacent if and only if $$1-xy$$ is not a unit in R. In this paper, up to isomorphism, we classify the rings R whose Jacobson graphs are toroidal. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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