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 $J,J_{ 1}$ for which we show that $J^{ k},$ and $J_{ 1}^{ k}$ have linear resolution if and only if $k\neq 2.$ The procedures we include in this work is encoded in computer algebra package CoCoA.
Categories: math.AC