A measure of non-sequential Cohen-Macaulayness of finitely generated modules

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• 作者：Le Thanh Nhan¹ ; ^{nhanlt2014@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Tran Duc Dung ^{ducdungdhkhtn88@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Tran Do Minh Chau ^{trandominhchau@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：13E05 ; 13C14 ; 13D45
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：468
• 期：Complete
• 页码：275-295
• 全文大小：454 K

文摘

Let M be a finitely generated module over a Noetherian local ring R. In this paper we introduce the notion of sequential polynomial type of M  , which is denoted by sp(M)$\mathrm{sp}(M)$, in order to measure how far M   is different from the sequential Cohen–Macaulayness. We study the sequential polynomial type under localization and 18ea7a0656e73a85960ddfa6f" title="Click to view the MathML source">m$\mathfrak{m}$-adic completion. We investigate an ascent–descent property of sequential polynomial type between M   and M/xM$M/xM$ for certain parameter x of M. When R   is a quotient of a Gorenstein local ring, we describe sp(M)$\mathrm{sp}(M)$ in term of the deficiency modules of M.