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

Published online by Cambridge University Press:  11 January 2016

Nguyên Công Minh
Affiliation:
Department of Mathematics Hanoi National University of Education, Hanoi, Vietnam, minhnc@hnue.edu.vn
Yukio Nakamura
Affiliation:
Department of Mathematics School of Science and Technology Meiji University, Kawasaki-shi 214-8571, Japan, ynakamu@meiji.ac.jp
Corresponding
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Abstract

Let S = K[x1,x2,…,xn ] be a polynomial ring over a field K. Let Δ be a simplicial complex whose vertex set is contained in {1, 2,…,n}. For an integer k ≥ 0, we investigate the k-Buchsbaum property of residue class rings S/I (t); and S/It for the Stanley-Reisner ideal I = IΔ . We characterize the k-Buchsbaumness of such rings in terms of the simplicial complex Δ and the power t. We also give a characterization in the case where I is the edge ideal of a simple graph.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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