Strong no-loop conjecture for algebras with two simples and radical cube zero

Bernt T. Jensen ¹

¹ Department of Pure Mathematics University of Leeds Leeds LS2 9JT, United Kingdom

Colloquium Mathematicum, Tome 102 (2005) no. 1, pp. 1-7

Résumé

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 ${\mathfrak r} ^3=0$.

Détail

DOI : 10.4064/cm102-1-1

Keywords: mit lambda artinian ring mathfrak denote its jacobson radical simple module finite projective dimension has self extensions mit lambda graded its radical simple modules mathfrak particular mit lambda finite dimensional algebra algebraically closed field simple modules mathfrak