Free resolution of powers of monomial ideals and Golod rings

• N. Altafi ^[1] ; N. Nemati ^[2] ; S. A. Seyed Fakhari ^[2] ; S. Yassemi ^[2]
  1. [1] Institute of Technology-SWEDEN
  2. [2] University of Tehran-IRAN
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 120, Nº 1, 2017, págs. 59-67
• Idioma: inglés
• DOI: 10.7146/math.scand.a-25504
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• Resumen

  • Let S=K[x1,…,xn] be the polynomial ring over a field 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≥1, the ideal Is has linear quotients with respect to a monomial order.