Resumen de Free resolution of powers of monomial ideals and Golod rings

N. Altafi, N. Nemati, S. A. Seyed Fakhari, Siamak Yassemi

• 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.