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Finiteness aspects of Gorenstein homological dimensions

Samir Bouchiba (2013)

Colloquium Mathematicae

We present an alternative way of measuring the Gorenstein projective (resp., injective) dimension of modules via a new type of complete projective (resp., injective) resolutions. As an application, we easily recover well known theorems such as the Auslander-Bridger formula. Our approach allows us to relate the Gorenstein global dimension of a ring R to the cohomological invariants silp(R) and spli(R) introduced by Gedrich and Gruenberg by proving that leftG-gldim(R) = maxleftsilp(R), leftspli(R),...

Finiteness of the strong global dimension of radical square zero algebras

Otto Kerner, Andrzej Skowroński, Kunio Yamagata, Dan Zacharia (2004)

Open Mathematics

The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density...

Gaussian and Prüfer conditions in bi-amalgamated algebras

Najib Mahdou, Moutu Abdou Salam Moutui (2020)

Czechoslovak Mathematical Journal

Let f : A → B and g : A → C be two ring homomorphisms and let J and J ' be ideals of B and C , respectively, such that f - 1 ( J ) = g - 1 ( J ' ) . In this paper, we investigate the transfer of the notions of Gaussian and Prüfer rings to the bi-amalgamation of A with ( B , C ) along ( J , J ' ) with respect to ( f , g ) (denoted by A ⋈ f , g ( J , J ' ) ) , introduced and studied by S. Kabbaj, K. Louartiti and M. Tamekkante in 2013. Our results recover well known results on amalgamations in C. A. Finocchiaro (2014) and generate new original examples of rings possessing these properties.

Homological dimensions and approximate contractibility for Köthe algebras

Alexei Yu. Pirkovskii (2010)

Banach Center Publications

We give a survey of our recent results on homological properties of Köthe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of Köthe algebras are also presented.

Homological dimensions for endomorphism algebras of Gorenstein projective modules

Aiping Zhang, Xueping Lei (2024)

Czechoslovak Mathematical Journal

Let A be a CM-finite Artin algebra with a Gorenstein-Auslander generator E , M be a Gorenstein projective A -module and B = End A M . We give an upper bound for the finitistic dimension of B in terms of homological data of M . Furthermore, if A is n -Gorenstein for 2 ≤ n < ∞ , then we show the global dimension of B is less than or equal to n plus the B -projective dimension of Hom A ( M , E ) . As an application, the global dimension of End A E is less than or equal to n .

Currently displaying 41 – 60 of 133