Displaying similar documents to “Finitistic dimension of artian rings with vanishing radical cube.”

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

Bernt T. Jensen (2005)

Colloquium Mathematicae

Similarity:

Let Λ be an artinian ring and let 𝔯 denote its Jacobson radical. We show that a simple module of finite projective dimension has no self-extensions when Λ is graded by its radical, with at most two simple modules and 𝔯⁴ = 0, in particular, when Λ is a finite-dimensional algebra over an algebraically closed field with at most two simple modules and 𝔯³ = 0.

On some Results Related to Köthe's Conjecture

Agata, Smoktunowicz (2001)

Serdica Mathematical Journal

Similarity:

The Köthe conjecture states that if a ring R has no nonzero nil ideals then R has no nonzero nil one-sided ideals. Although for more than 70 years significant progress has been made, it is still open in general. In this paper we survey some results related to the Köthe conjecture as well as some equivalent problems.