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A Generalized Serre's Condition. (arXiv:1710.02631v1 [math.AC])

来源于:arXiv
Throughout, let $R$ be a commutative Noetherian ring. A ring $R$ satisfies Serre's condition $(S_{\ell})$ if for all $P \in \textrm{ Spec }R,$ $\textrm{ depth } R_P \geq \min \{ \ell , \dim R_P \}$. Serre's condition has been a topic of expanding interest. In this paper, we examine a generalization of Serre's condition $(S_{\ell}^j)$. We say a ring satisfies $(S_{\ell}^j)$ when $\textrm{ depth } R_P \geq \min \{ \ell , \dim R_P -j \}$ for all $P \in \textrm{ Spec }R$. We prove generalizations of results for rings satisfying Serre's condition. 查看全文>>