## Rocky Mountain Journal of Mathematics

- Rocky Mountain J. Math.
- Volume 47, Number 2 (2017), 621-635.

### Sequentially Cohen-Macaulayness of bigraded modules

#### Abstract

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.

#### Article information

**Source**

Rocky Mountain J. Math., Volume 47, Number 2 (2017), 621-635.

**Dates**

First available in Project Euclid: 18 April 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.rmjm/1492502553

**Digital Object Identifier**

doi:10.1216/RMJ-2017-47-2-621

**Mathematical Reviews number (MathSciNet)**

MR3635377

**Zentralblatt MATH identifier**

06715764

**Subjects**

Primary: 13C14: Cohen-Macaulay modules [See also 13H10] 13D45: Local cohomology [See also 14B15] 16W50: Graded rings and modules 16W70: Filtered rings; filtrational and graded techniques

**Keywords**

Dimension filtration sequentially Cohen-Macaulay cohomological dimension bigraded modules hypersurface rings

#### Citation

Rahimi, Ahad. Sequentially Cohen-Macaulayness of bigraded modules. Rocky Mountain J. Math. 47 (2017), no. 2, 621--635. doi:10.1216/RMJ-2017-47-2-621. https://projecteuclid.org/euclid.rmjm/1492502553