Free resolution of powers of monomial ideals and Golod rings - Altafi, N.; Nemati, N.; Seyed Fakhari, S. A.; Yassemi, S. (MATHEMATICA SCANDINAVICA, 2017)
Let S = K[x_1, …, x_n] 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 I^s has linear quotients with respect to a monomial order.