Sequentially Cohen-Macaulayness of bigraded modules
| Autor: | Ahad Rahimi |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics::Theory
13D45 cohomological dimension General Mathematics Polynomial ring 0211 other engineering and technologies Field (mathematics) 02 engineering and technology Cohomological dimension Commutative Algebra (math.AC) bigraded modules 01 natural sciences Combinatorics FOS: Mathematics Mathematics - Combinatorics Mathematics::Metric Geometry Computer Science::Symbolic Computation Finitely-generated abelian group 0101 mathematics Mathematics sequentially Cohen-Macaulay 13C14 Mathematics::Commutative Algebra 010102 general mathematics 021107 urban & regional planning Mathematics - Commutative Algebra hypersurface rings Hypersurface 16W70 Combinatorics (math.CO) Dimension filtration 16W50 |
| Zdroj: | Rocky Mountain J. Math. 47, no. 2 (2017), 621-635 |
| ISSN: | 0035-7596 |
| DOI: | 10.1216/rmj-2017-47-2-621 |
| Popis: | Let $K$ be a field, $S=K[x_1,\ldots ,x_m, y_1,\ldots , y_n]$ a standard bigraded polynomial ring, and $M$ a finitely generated bigraded $S$-module. In this paper, we study the sequentially Cohen-Macaulayness of~$M$ with respect to $Q=(y_1,\ldots ,y_n)$. We characterize the sequentially Cohen-Macaulayness of $L\otimes _KN$ with respect to $Q$ as an $S$-~module when $L$ and $N$ are non-zero finitely generated graded modules over $K[x_1, \ldots , x_m]$ and $K[y_1, \ldots , y_n]$, respectively. All hypersurface rings that are sequentially Cohen-Macaulay with respect to $Q$ are classified. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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