en تخصصي Special پژوهشي Research paper <p></p> <p>Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper we compute powers of the genearlized mixed product ideals and show that L^k&nbsp; have a linear resolution if and only if I^k have a linear resolution for all k. We also introduce the generalized mixed polymatroidal ideals and prove that powers and monomial localizations of a generalized mixed polymatroidal ideal is again generalized mixed polymatroidal ideal.</p> Free resolutoins, Graded betti numbers, Monomial ideals. 127 134 http://ijmsi.ir/browse.php?a_code=A-10-2145-1&slc_lang=en&sid=1 A. Tehranian tehranian@srbiau.ac.ir 10031947532846007044 10031947532846007044 Yes Department of mathematics, Science and Research branch, Islamic azad university, Tehran Iran R. Moghimipor roya_moghimipour@yahoo.com 10031947532846007045 10031947532846007045 No Department of mathematics, Science and Research branch, Islamic azad university, Tehran Iran