## Nagoya Mathematical Journal

### On the $k$-Buchsbaum property of powers of Stanley–Reisner ideals

#### Abstract

Let $S=K[x_{1},x_{2},\ldots,x_{n}]$ be a polynomial ring over a field $K$. Let ${\Delta}$ be a simplicial complex whose vertex set is contained in $\{1,2,\ldots,n\}$. For an integer $k\geq0$, we investigate the $k$-Buchsbaum property of residue class rings $S/I^{(t)}$ and $S/I^{\,t}$ for the Stanley–Reisner ideal $I=I_{{\Delta}}$. We characterize the $k$-Buchsbaumness of such rings in terms of the simplicial complex ${\Delta}$ and the power $t$. We also give a characterization in the case where $I$ is the edge ideal of a simple graph.

#### Article information

Source
Nagoya Math. J., Volume 213 (2014), 127-140.

Dates
First available in Project Euclid: 17 December 2013

https://projecteuclid.org/euclid.nmj/1387313477

Digital Object Identifier
doi:10.1215/00277630-2394073

Mathematical Reviews number (MathSciNet)
MR3161406

Zentralblatt MATH identifier
1291.13041

#### Citation

Minh, Nguyên Công; Nakamura, Yukio. On the $k$ -Buchsbaum property of powers of Stanley–Reisner ideals. Nagoya Math. J. 213 (2014), 127--140. doi:10.1215/00277630-2394073. https://projecteuclid.org/euclid.nmj/1387313477

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