On graded Going down domains
| Autor: | Sahandi, Parviz, Shirmohammadi, Nematollah |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\Gamma$ be a torsionless commutative cancellative monoid and $R =\bigoplus_{\alpha \in \Gamma}R_{\alpha}$ be a $\Gamma$-graded integral domain. In this paper, we introduce the notion of graded going-down domains. Among other things, we provide an equivalent condition for graded-Pr\"{u}fer domains in terms of graded going-down and graded finite-conductor domains. We also characterize graded going-down domains by means of graded divided domains. As an application, we show that the graded going-down property is stable under factor domains. Comment: Final version, to appear in JAA |
| Databáze: | arXiv |
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