On Modules of Linear Type

Abstract

Let A be an m × n matrix with entries in a Noetherian ring R, where m,n are positive integers such that m ≤ n. By M, we denote the cokernel of the R-linear map Rm → Rn defined by tA . The purpose of this paper is to give an elementary proof to the result due to Avramov (J. Algebra 73, 248–263, 1981) that characterizes the condition for M to be a module of linear type in terms of determinantal ideals of A.