Displaying similar documents to “Towards a theory of Bass numbers with application to Gorenstein algebras”

States on basic algebras

Ivan Chajda, Helmut Länger (2017)

Mathematica Bohemica

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States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which...

On B-algebras

J. Neggers, Hee Sik Kim (2002)

Matematički Vesnik

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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.

Nonlinear separable equations in linear spaces and commutative Leibniz algebras

D. Przeworska-Rolewicz (2010)

Annales Polonici Mathematici

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We consider nonlinear equations in linear spaces and algebras which can be solved by a "separation of variables" obtained due to Algebraic Analysis. It is shown that the structures of linear spaces and commutative algebras (even if they are Leibniz algebras) are not rich enough for our purposes. Therefore, in order to generalize the method used for separable ordinary differential equations, we have to assume that in algebras under consideration there exist logarithmic mappings. Section...

On finiteness conditions for subalgebras with zero multiplication

Jan Krempa (2005)

Colloquium Mathematicae

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Let F be a commutative ring with unit. In this paper, for an associative F-algebra A we study some properties forced by finite length or DCC condition on F-submodules of A that are subalgebras with zero multiplication. Such conditions were considered earlier when F was either a field or the ring of rational integers. In the final section, we consider algebras with maximal commutative subalgebras of finite length as F-modules and obtain some results parallel to those known for ACC condition...

The global basie dimension of artin rings

Hagen Meltzer, Andrzej Skowroński

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CONTENTS1. Introduction.............52. Basic dimension of artin rings................73. Cobasic dimension of artin rings............84. Basic dimension of algebras stably equivalent to an hereditary artin algebra............125. Hereditary artin algebras of global basic and cobasic dimension 1....................176. Global basic and cobasic dimensions of radical squared zero algebras............34References...............43

On the classification of the real flexible division algebras

Erik Darpö (2006)

Colloquium Mathematicae

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We investigate the class of finite-dimensional real flexible division algebras. We classify the commutative division algebras, completing an approach by Althoen and Kugler. We solve the isomorphism problem for scalar isotopes of quadratic division algebras, and classify the generalised pseudo-octonion algebras. In view of earlier results by Benkart, Britten and Osborn and Cuenca Mira et al., this reduces the problem of classifying the real flexible division algebras...