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On Modules of Linear Type

Kosuke Fukumuro , Hirofumi Kume , $icon-email$ 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 $R^{m} ⟶ R^{n}$ 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 $A$ .

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On Modules of Linear Type

Abstract