Document Type : Original Manuscript


Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran and School of Mathematics, Institute for research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran.


In this paper, we introduce the class of ideals with $(d_1,\ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,\ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.