On linear resolution of powers of an ideal

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In this paper we give a generalization of a result of Herzog, Hibi, and Zheng providing an upper bound for regularity of powers of an ideal. As the main result of the paper, we give a simple criterion in terms of Rees algebra of a given ideal to show that high enough powers of this ideal have linear resolution. We apply the criterion to two important ideals J,J₁ for which we show that Jᵏ, and J₁ᵏ have linear resolution if and only if k≠ 2. The procedures we include in this work is encoded in computer algebra package CoCoA.