Strong no-loop conjecture for algebras with two simples and radical cube zero
Volume 102 / 2005
Colloquium Mathematicum 102 (2005), 1-7
MSC: 16D10, 16E10.
DOI: 10.4064/cm102-1-1
Abstract
Let ${\mit\Lambda}$ be an artinian ring and let ${\mathfrak r}$ denote its Jacobson radical. We show that a simple module of finite projective dimension has no self-extensions when ${\mit\Lambda}$ is graded by its radical, with at most two simple modules and ${\mathfrak r} ^4 = 0$, in particular, when ${\mit\Lambda}$ is a finite-dimensional algebra over an algebraically closed field with at most two simple modules and ${\mathfrak r} ^3=0$.
