表示直向代数的模的刻画

A characterization of modules for representation-directed algebras

设Λ是有限域k上的表示直向代数.对任意有限生成右Λ-模M,本文利用Hall数定义了模M的一个同构不变量,证明了该不变量可以在同构意义下唯一确定模M,从而揭示了表示直向代数上的模的Hall数与模的同构类分类问题的内在联系.

LetΛbe a representation-directed algebra over finite field k.For arbitrary finitely generated rightΛ-module M,we define an invariant for M by using Hall numbers associated to M.It is proved that the invariant uniquely determines the module M up to isomorphism,thus revealed the relation between the Hall number and the isomorphic classification problem of the module.