Free resolution of powers of monomial ideals and Golod rings

  • N. Altafi
  • N. Nemati
  • S. A. Seyed Fakhari
  • S. Yassemi

Abstract

Let $S = \mathbb{K}[x_1, \dots, x_n]$ be the polynomial ring over a field $\mathbb{K}$. In this paper we present a criterion for componentwise linearity of powers of monomial ideals. In particular, we prove that if a square-free monomial ideal $I$ contains no variable and some power of $I$ is componentwise linear, then $I$ satisfies the gcd condition. For a square-free monomial ideal $I$ which contains no variable, we show that $S/I$ is a Golod ring provided that for some integer $s\geq 1$, the ideal $I^s$ has linear quotients with respect to a monomial order.

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Published
2017-02-23
How to Cite
Altafi, N., Nemati, N., Seyed Fakhari, S. A., & Yassemi, S. (2017). Free resolution of powers of monomial ideals and Golod rings. MATHEMATICA SCANDINAVICA, 120(1), 59-67. https://doi.org/10.7146/math.scand.a-25504
Section
Articles