**On Modules of Linear Type **

* Kosuke Fukumuro, Hirofumi Kume, Koji Nishida *

**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 *R* ^{ m } → *R* ^{ n } defined by ^{ t } *A* . 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*.