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

Tom 102 / 2005

Bernt T. Jensen Colloquium Mathematicum 102 (2005), 1-7 MSC: 16D10, 16E10. DOI: 10.4064/cm102-1-1

Streszczenie

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

Autorzy

  • Bernt T. JensenDepartment of Pure Mathematics
    University of Leeds
    Leeds LS2 9JT, United Kingdom
    e-mail

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