论文标题
尺寸6的短局部代数，具有非预定反射模块
The short local algebras of dimension 6 with non-projective reflexive modules
论文作者
论文摘要
让$ a $是一个有限维度的本地代数，在代数封闭的字段上，让$ j $是$ A的根本。投影模块总是反射的，而代数为自注，如果所有模块都是反身的。如果$ a $不是自我注射，我们讨论了非预定反射模块的存在。我们假设$ a $很短（这意味着$ j^3 = 0 $）。在与Zhang PU的联合论文中，已经证明6是可能发生的$ a $的最小尺寸，在这种情况下，必须满足以下条件：$ j^2 $既是左socle又是$ a $ a $的左socle，并且没有长度3的统一理想。
Let $A$ be a finite-dimensional local algebra over an algebraically closed field, let $J$ be the radical of $A.$ The modules we are interested in are the finitely generated left $A$-modules. Projective modules are always reflexive, and an algebra is self-injective iff all modules are reflexive. We discuss the existence of non-projective reflexive module in case $A$ is not self-injective. We 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 3. The present paper is devoted to show the converse.
