The extended zero-divisor graph of the amalgamated duplication of a ring along an ideal
| Autor: | Alaoui, Brahim El, L'hamri, Raja |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $R$ be a commutative ring and $I$ be an ideal of $R$. The amalgamated duplication of $R$ along $I$ is the subring $R\Join I:=\{(r,r+i)| r\in R, i\in I\}$ of $R\times R$. This paper investigates the extended zero-divisor graph of the amalgamated duplication of $R$ along $I$. The purpose of this work is to study when $\overline{\Gamma}(R\Join I)$ and $\Gamma(R\Join I)$ coincide, to characterize when $\overline{\Gamma}(R\Join I)$ is complete, and to compute the diameter and the girth of $\overline{\Gamma}(R\Join I)$. Comment: 10 pages, 2 figures |
| Databáze: | arXiv |
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