Let S = \mathbbK[x_{1}, ..., x_{n}] 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 squarefree monomial ideal I contains no variable and some power of I is componentwise linear, then I satisfies the gcd condition. For a squarefree 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.
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