Free resolution of powers of monomial ideals and Golod rings

• Let S = Kdbl[x1,⋯, xn] be the polynomial ring over a field Kdbl. In this paper we present a criterion for componentwise linearity of powers of monomial ideals. In particular, we prove that if a squarefree 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.

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NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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