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Fragmented deformations of primitive multiple curves

Jean-Marc Drézet (2013)

Open Mathematics

A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization...

Fredholm spectrum and growth of cohomology groups

Jörg Eschmeier (2008)

Studia Mathematica

Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let σ F ( T ) = σ ( T ) ∖ σ e ( T ) be the non-essential spectrum of T. We show that, for each connected component M of the manifold R e g ( σ F ( T ) ) of all smooth points of σ F ( T ) , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups H p ( ( z - T ) k , E ) grow at least like the sequence ( k d ) k ≥ 1 with d = dim M.

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.

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