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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.

G-dimension over local homomorphisms with respect to a semi-dualizing complex

Wu Dejun (2014)

Czechoslovak Mathematical Journal

We study the G-dimension over local ring homomorphisms with respect to a semi-dualizing complex. Some results that track the behavior of Gorenstein properties over local ring homomorphisms under composition and decomposition are given. As an application, we characterize a dualizing complex for R in terms of the finiteness of the G-dimension over local ring homomorphisms with respect to a semi-dualizing complex.

Generalized tilting modules over ring extension

Zhen Zhang (2019)

Czechoslovak Mathematical Journal

Let Γ be a ring extension of R . We show the left Γ -module U = Γ ⊗ R C with the endmorphism ring End Γ U = Δ is a generalized tilting module when R C is a generalized tilting module under some conditions.

Grothendieck ring of quantum double of finite groups

Jingcheng Dong (2010)

Czechoslovak Mathematical Journal

Let k G be a group algebra, and D ( k G ) its quantum double. We first prove that the structure of the Grothendieck ring of D ( k G ) can be induced from the Grothendieck ring of centralizers of representatives of conjugate classes of G . As a special case, we then give an application to the group algebra k D n , where k is a field of characteristic 2 and D n is a dihedral group of order 2 n .

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