Erratum to : “The finite free extension of artinian $K$-algebras with the strong Lefschetz property” [Rend. Sem. Mat. Univ. Padova 110 (2003), 119–146]

Tadahito Harima; Junzo Watanabe

The search session has expired. Please query the service again.

Displaying similar documents to “Erratum to : “The finite free extension of artinian $K$ -algebras with the strong Lefschetz property” [Rend. Sem. Mat. Univ. Padova 110 (2003), 119–146]”

Standardly stratified split and lower triangular algebras

Eduardo do N. Marcos, Hector A. Merklen, Corina Sáenz (2002)

Colloquium Mathematicae

Similarity:

In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for $A = [\begin{matrix} U & 0 \\ M & V \end{matrix}]$ , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and $_{V} M$ is a good V-module.

Leibniz $A$ -algebras

David A. Towers (2020)

Communications in Mathematics

Similarity:

A finite-dimensional Lie algebra is called an $A$ -algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras. ...

Hyper BCI-algebras

Xiao Long Xin (2006)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

We introduce the concept of a hyper BCI-algebra which is a generalization of a BCI-algebra, and investigate some related properties. Moreover we introduce a hyper BCI-ideal, weak hyper BCI-ideal, strong hyper BCI-ideal and reflexive hyper BCI-ideal in hyper BCI-algebras, and give some relations among these hyper BCI-ideals. Finally we discuss the relations between hyper BCI-algebras and hyper groups, and between hyper BCI-algebras and hyper $H_{v}$ -groups.

Derived equivalences between generalized matrix algebras

QingHua Chen, HongJin Liu (2020)

Czechoslovak Mathematical Journal

Similarity:

We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the $n$ -replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.

Division algebras that generalize Dickson semifields

Daniel Thompson (2020)

Communications in Mathematics

Similarity:

We generalize Knuth’s construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension $2 s^{2}$ by doubling central division algebras of degree $s$ . Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

On a Construction of ModularGMS-algebras

Abd El-Mohsen Badawy (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety ${\underset{̲}{𝐊}}_{2}$ by means of ${\underset{̲}{K}}_{2}$ -quadruples. We also characterize isomorphisms of these algebras by means of ${\underset{̲}{K}}_{2}$ -quadruples.

Generalized Post algebras and their application to some infinitary many-valued logics

Cat-Ho Nguyen

Similarity:

CONTENTSIntroduction............................................................................................................................................................................... 5Part I. A generalization of Post algebras............................................................................................................................. 7 1. Definition and characterization of generalized Post algebras............................................. 7 2. Post...

An upper bound for the distance to finitely generated ideals in Douglas algebras

Pamela Gorkin, Raymond Mortini, Daniel Suárez (2001)

Studia Mathematica

Similarity:

Let f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for $H^{\infty}$ to arbitrary Douglas algebras.

Some remarks on $Q$ -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

Similarity:

We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that $ℓ^{p}$ , $(1 \leq p \leq \infty)$ are $Q$ algebras and that $A_{n} = ℨ L^{1} (Z; 1 + | n |^{α})$ is a $Q$ -algebra if and only if $α > 1 / 2$ .

A geometric approach to full Colombeau algebras

R. Steinbauer (2010)

Banach Center Publications

Similarity:

We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view of the construction of the intrinsically defined algebra $\hat{} (M)$ on the manifold M given in [gksv].

Engel BCI-algebras: an application of left and right commutators

Ardavan Najafi, Arsham Borumand Saeid (2021)

Mathematica Bohemica

Similarity:

We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of $n$ -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type $2$ is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is...

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

Similarity:

A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of $G^{\infty}$ -generalized functions class are given. A straightforward relationship between the classical and the generalized...

Metric generalizations of Banach algebras

W. Żelazko

Similarity:

CONTENTSPRELIMINARIES§ 0. Introduction.......................................................................................................................................................................3§ 1. Definitions and notation.................................................................................................................................................5Chapter ILOCALLY BOUNDED ALGEBRAS§ 2. Basic facts and examples..............................................................................................................................................6§...

The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra

Edward L. Green, Nicole Snashall (2006)

Colloquium Mathematicae

Similarity:

This paper studies the Hochschild cohomology of finite-dimensional monomial algebras. If Λ = K/I with I an admissible monomial ideal, then we give sufficient conditions for the existence of an embedding of $K [x ₁, . . ., x_{r}] / ⟨ x_{a} x_{b} f o r a \neq b ⟩$ into the Hochschild cohomology ring HH*(Λ). We also introduce stacked algebras, a new class of monomial algebras which includes Koszul and D-Koszul monomial algebras. If Λ is a stacked algebra, we prove that $H H * (Λ) / ≅ K [x ₁, . . ., x_{r}] / ⟨ x_{a} x_{b} f o r a \neq b ⟩$ , where is the ideal in HH*(Λ) generated by the homogeneous nilpotent elements....

On some properties of the upper central series in Leibniz algebras

Leonid A. Kurdachenko, Javier Otal, Igor Ya. Subbotin (2019)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

This article discusses the Leibniz algebras whose upper hypercenter has finite codimension. It is proved that such an algebra $L$ includes a finite dimensional ideal $K$ such that the factor-algebra $L / K$ is hypercentral. This result is an extension to the Leibniz algebra of the corresponding result obtained earlier for Lie algebras. It is also analogous to the corresponding results obtained for groups and modules.

Displaying similar documents to “Erratum to : “The finite free extension of artinian K -algebras with the strong Lefschetz property” [Rend. Sem. Mat. Univ. Padova 110 (2003), 119–146]”

Displaying similar documents to “Erratum to : “The finite free extension of artinian $K$ -algebras with the strong Lefschetz property” [Rend. Sem. Mat. Univ. Padova 110 (2003), 119–146]”