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A class of quasitilted rings that are not tilted

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

Colloquium Mathematicae

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.

A duality result for almost split sequences

Lidia Hügel, Helmut Valenta (1999)

Colloquium Mathematicae

Over an artinian hereditary ring R, we discuss how the existence of almost split sequences starting at the indecomposable non-injective preprojective right R-modules is related to the existence of almost split sequences ending at the indecomposable non-projective preinjective left R-modules. This answers a question raised by Simson in [27] in connection with pure semisimple rings.

A family of noetherian rings with their finite length modules under control

Markus Schmidmeier (2002)

Czechoslovak Mathematical Journal

We investigate the category mod Λ of finite length modules over the ring Λ = A k Σ , where Σ is a V-ring, i.e. a ring for which every simple module is injective, k a subfield of its centre and A an elementary k -algebra. Each simple module E j gives rise to a quasiprogenerator P j = A E j . By a result of K. Fuller, P j induces a category equivalence from which we deduce that mod Λ j b a d h b o x P j . As a consequence we can (1) construct for each elementary k -algebra A over a finite field k a nonartinian noetherian ring Λ such that mod A mod Λ , (2) find twisted...

A Morita equivalence for Hilbert C*-modules

Maria Joiţa, Mohammad Sal Moslehian (2012)

Studia Mathematica

We introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate the properties of the new Morita equivalence. We apply our results to study continuous actions of locally compact groups on full Hilbert C*-modules. We also present an extension of Green's theorem in the context of Hilbert C*-modules.

A Morita type theorem for a sort of quotient categories

Simion Breaz (2005)

Czechoslovak Mathematical Journal

We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.

A note on tilting sequences

Clezio Braga, Flávio Coelho (2008)

Open Mathematics

We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.

Actions of parabolic subgroups in GL_n on unipotent normal subgroups and quasi-hereditary algebras

Thomas Brüstle, Lutz Hille (2000)

Colloquium Mathematicae

Let R be a parabolic subgroup in G L n . It acts on its unipotent radical R u and on any unipotent normal subgroup U via conjugation. Let Λ be the path algebra k t of a directed Dynkin quiver of type with t vertices and B a subbimodule of the radical of Λ viewed as a Λ-bimodule. Each parabolic subgroup R is the group of automorphisms of an algebra Λ(d), which is Morita equivalent to Λ. The action of R on U can be described using matrices over the bimodule B. The advantage of this description is that each...

Algebras stably equivalent to trivial extensions of hereditary algebras of type à n

Zygmunt Pogorzały (1993)

Colloquium Mathematicae

The study of stable equivalences of finite-dimensional algebras over an algebraically closed field seems to be far from satisfactory results. The importance of problems concerning stable equivalences grew up when derived categories appeared in representation theory of finite-dimensional algebras [8]. The Tachikawa-Wakamatsu result [17] also reveals the importance of these problems in the study of tilting equivalent algebras (compare with [1]). In fact, the result says that if A and B are tilting...

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