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On Modules of Linear Type
Kosuke Fukumuro
,
Hirofumi Kume
,
Koji Nishida
Abstract
Let $A$ be an $m \times n$ matrix with entries in a Noetherian ring $R$, where $m, n$ are positive integers such that $m \leq n$. By $M$ we denote the cokernel of the $R$-linear map $R^m \longrightarrow R^n$ 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 $A$.