Displaying similar documents to “On the Finistic dimension conjecture for Artinian Rings.”

On hereditary rings and the pure semisimplicity conjecture II: Sporadic potential counterexamples

José L. García (2015)

Colloquium Mathematicae

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It was shown in [Colloq. Math. 135 (2014), 227-262] that the pure semisimplicity conjecture (briefly, pssC) can be split into two parts: first, a weak pssC that can be seen as a purely linear algebra condition, related to an embedding of division rings and properties of matrices over those rings; the second part is the assertion that the class of left pure semisimple sporadic rings (ibid.) is empty. In the present article, we characterize the class of left pure semisimple sporadic rings...

On hereditary artinian rings and the pure semisimplicity conjecture: rigid tilting modules and a weak conjecture

José L. García (2014)

Colloquium Mathematicae

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A weak form of the pure semisimplicity conjecture is introduced and characterized through properties of matrices over division rings. The step from this weak conjecture to the full pure semisimplicity conjecture would be covered by proving that there do not exist counterexamples to the conjecture in a particular class of rings, which is also studied.

A class of quasitilted rings that are not tilted

Riccardo Colpi, Kent R. Fuller, Enrico Gregorio (2006)

Colloquium Mathematicae

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Based on the work of D. Happel, I. Reiten and S. Smalø on quasitilted artin algebras, the first two authors recently introduced the notion of quasitilted rings. Various authors have presented examples of quasitilted artin algebras that are not tilted. Here we present a class of right quasitilted rings that not right tilted, and we show that they satisfy a condition that would force a quasitilted artin algebra to be tilted.

Pere Menal i Brufal, 1951-1991.

Joaquim Bruna, Warren Dicks (1992)

Publicacions Matemàtiques

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Pere Menal, Professor of Algebra at the Universitat Autònoma de Barcelona, died in a traffic accident on April 4th, 1991. His colleagues in the Mathematics Department of the UAB strongly felt the need to pay a tribute to his memory, and decided then to dedicate this, the Autumn 1992 issue of the departmental journal, to his memory.