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Closed extensions of R-modules in the case of a semi-artinian ring R

Frans Loonstra (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si considerano le estensioni chiuse B di un R -modulo A mediante un R -modulo C nel caso in cui R sia un anello semi-artiniano, cioè un anello R con la proprietà che per ogni quoziente ( R / I ) ≠ 0 sia soc ( R / I ) ≠ 0 . Tali estensioni sono caratterizzate dal fatto che A deve essere un sottomodulo semi-puro di B .

Coalgebras, comodules, pseudocompact algebras and tame comodule type

Daniel Simson (2001)

Colloquium Mathematicae

We develop a technique for the study of K-coalgebras and their representation types by applying a quiver technique and topologically pseudocompact modules over pseudocompact K-algebras in the sense of Gabriel [17], [19]. A definition of tame comodule type and wild comodule type for K-coalgebras over an algebraically closed field K is introduced. Tame and wild coalgebras are studied by means of their finite-dimensional subcoalgebras. A weak version of the tame-wild dichotomy theorem of Drozd [13]...

Codimension B-W d’un idéal à droite non nul de A 1 ( ℂ )

Mathias Konan Kouakou (2005)

Bulletin de la Société Mathématique de France

Soit A 1 ( ℂ ) la première algèbre de Weyl sur ℂ . La codimension B-W d’un idéal à droite non nul I de A 1 ( ℂ ) a été introduite par Yuri Berest et George Wilson. Nous montrons d’une part que cette codimension est invariante par la relation de Stafford : si x ∈ Q 1 = Frac ( A 1 ( ℂ ) ) , le corps de fractions de A 1 ( ℂ ) , et si σ ∈ Aut ( A 1 ( ℂ ) ) , le groupe des ℂ -automorphismes de A 1 ( ℂ ) , sont tels que J = x σ ( I ) soit un idéal à droite de A 1 ( ℂ ) , alors codim I = codim x σ ( I ) . Nous relions d’autre part la codimension d’un idéal I à la codimension de Gail Letzter-Makar Limanov, de End ( I ) , l’anneau des endomorphismes...

Cohen-Macaulay modules over two-dimensional graph orders

Klaus Roggenkamp (1999)

Colloquium Mathematicae

For a split graph order ℒ over a complete local regular domain 𝒪 of dimension 2 the indecomposable Cohen-Macaulay modules decompose - up to irreducible projectives - into a union of the indecomposable Cohen-Macaulay modules over graph orders of type •—• . There, the Cohen-Macaulay modules filtered by irreducible Cohen-Macaulay modules are in bijection to the homomorphisms ϕ : 𝒪 L ( μ ) → 𝒪 L ( ν ) under the bi-action of the groups ( G l ( μ , 𝒪 L ) , G l ( ν , 𝒪 L ) ) , where 𝒪 L = 𝒪 / 〈 π 〉 for a prime π. This problem strongly depends on the nature of 𝒪 L . If 𝒪 L is regular,...

Commutativity theorems for rings with differential identities on Jordan ideals

L. Oukhtite, A. Mamouni, Mohammad Ashraf (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper we investigate commutativity of ring R with involution ' * ' which admits a derivation satisfying certain algebraic identities on Jordan ideals of R . Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.

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