The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules
作者机构：Fakultät für MathematikUniversität BielefeldPO Box 10013133501 BielefeldGermany
出 版 物：《Communications in Mathematics and Statistics》 (数学与统计通讯（英文）)
年 卷 期：2023年第11卷第2期
页 面：195-227页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：Open Access funding enabled and organized by Projekt DEAL
主 题：Short local algebra Reflexive module Gorenstein-projective module Bristle Atom Bar Bristle-bar layout
摘 要：Let A be a finite-dimensional local algebra over an algebraically closed field,let J be the radical of *** modules we are interested in are the finitely generated left *** are always reflexive,and an algebra is self-injective iff allmodules are *** discuss the existence of non-projective reflexive modules in case A is not *** assume that A is short(this means that J^(3)=0).In a joint paper with Zhang Pu,it has been shown that 6 is the smallest possible dimension of A that can occur and that in this case the following conditions have to be satisfied:J^(2)is both the left socle and the right socle of A and there is no uniform ideal of length *** present paper is devoted to showing the converse.
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