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Domestic iterated one-point extensions of algebras by two-ray modules

Grzegorz Bobiński, Andrzej Skowroński (2003)

Open Mathematics

In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of...

Drinfeld doubles via derived Hall algebras and Bridgeland's Hall algebras

Fan Xu, Haicheng Zhang (2021)

Czechoslovak Mathematical Journal

Let 𝒜 be a finitary hereditary abelian category. We give a Hall algebra presentation of Kashaev’s theorem on the relation between Drinfeld double and Heisenberg double. As applications, we obtain realizations of the Drinfeld double Hall algebra of 𝒜 via its derived Hall algebra and Bridgeland’s Hall algebra of m -cyclic complexes.

Dual dimension of modules over normalizing extensions.

Ahmad Shamsuddin (1993)

Publicacions Matemàtiques

Let S = Σi=1n Rai be a finite normalizing extension of R and suppose that SM is a left S-module. Denote by crk(A) the dual Goldie dimension of the module A. We show that crk(RM) ≤ n · crk(SM) if either SM is artinian or the group homomorphism M → aiM given by x → aix is an isomorphism.

Dual modules and reflexive modules with respect to a semidualizing module

Lixin Mao (2024)

Czechoslovak Mathematical Journal

Let C be a semidualizing module over a commutative ring. We first investigate the properties of C -dual, C -torsionless and C -reflexive modules. Then we characterize some rings such as coherent rings, Π -coherent rings and FP-injectivity of C using C -dual, C -torsionless and C -reflexive properties of some special modules.

Dually steady rings

Robert El Bashir, Tomáš Kepka, Jan Žemlička (2011)

Acta Universitatis Carolinae. Mathematica et Physica

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