IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 13701
School of Mathematics
Title: Free resolution of powers of monomial ideals and Golod rings
Author(s):
 1 . S. A. Seyed Fakhari 2 . S. Yassemi (Joint with N. Altafi and N. Nemati)
Status: To Appear
Journal: Math. Scand.
Supported by: IPM
Abstract:
Let S = \mathbbK[x1, ..., xn] be the polynomial ring over a field \mathbbK. 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.