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

Ardavan Najafi; Arsham Borumand Saeid

Displaying similar documents to “Engel BCI-algebras: an application of left and right commutators”

$ω$ -compact elements of normed algebras

Gh. Constantin (1973)

Matematički Vesnik

Similarity:

Centralizers for subsets of normed algebras

Bertram Yood (2000)

Studia Mathematica

Similarity:

Let G be the set of invertible elements of a normed algebra A with an identity. For some but not all subsets H of G we have the following dichotomy. For x ∈ A either $c x c^{- 1} = x$ for all c ∈ H or $s u p ∥ c x c^{- 1} ∥ : c \in H = \infty$ . In that case the set of x ∈ A for which the sup is finite is the centralizer of H.

A representation theorem for tense $n \times m$ -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

Similarity:

In 2000, Figallo and Sanza introduced $n \times m$ -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$ -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class $_{n \times m}$ of tense $n \times m$ -valued Łukasiewicz-Moisil algebras (or tense LM $_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...

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.

Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{matrix} F_{m}^{1} \end{matrix}$ nilradical

L.M. Camacho, B.A. Omirov, K.K. Masutova, I.M. Rikhsiboev (2017)

Open Mathematics

Similarity:

All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 $\begin{matrix} F_{m}^{1} \end{matrix}$ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 $\begin{matrix} F_{m}^{1} \end{matrix}$ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.

On generalized Beurling’s theorem and symmetry of $L_{1}$ -group algebras

Zenobia Anusiak (1971)

Colloquium Mathematicae

Similarity:

On cardinalities of algebras of formulas for $ω_{0}$ -categorical theories

Jan Waszkiewicz (1973)

Colloquium Mathematicae

Similarity:

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§...

$ℵ_{0}$ -categoricity of products of 1-unary algebras

Philip Olin (1975)

Colloquium Mathematicae

Similarity:

Matrix representation of finite effect algebras

Grzegorz Bińczak, Joanna Kaleta, Andrzej Zembrzuski (2023)

Kybernetika

Similarity:

In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra $E$ we construct set of matrices $M (E)$ in such a way that effect algebras $E_{1}$ and $E_{2}$ are isomorphic if and only if $M (E_{1}) = M (E_{2})$ . The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most $8$ .

Transfer of derived equivalences from subalgebras to endomorphism algebras II

Shengyong Pan, Jiahui Yu (2024)

Czechoslovak Mathematical Journal

Similarity:

We investigate derived equivalences between subalgebras of some $Φ$ -Auslander-Yoneda algebras from a class of $n$ -angles in weakly $n$ -angulated categories. The derived equivalences are obtained by transferring subalgebras induced by $n$ -angles to endomorphism algebras induced by approximation sequences. Then we extend our constructions in T. Brüstle, S. Y. Pan (2016) to $n$ -angle cases. Finally, we give an explicit example to illustrate our result.

Singularity categories of skewed-gentle algebras

Xinhong Chen, Ming Lu (2015)

Colloquium Mathematicae

Similarity:

Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let $(Q^{s g}, I^{s g})$ and $(Q^{g}, I^{g})$ be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra $K Q^{s g} / ⟨ I^{s g} ⟩$ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of $K Q^{g} / ⟨ I^{g} ⟩$ . As a corollary, we find that $g l d i m K Q^{s g} / ⟨ I^{s g} ⟩ < \infty$ if and only if $g l d i m K Q / ⟨ I ⟩ < \infty$ if and only if $g l d i m K Q^{g} / ⟨ I^{g} ⟩ < \infty$ .

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.

Quantised ${𝔰𝔩}_{2}$ -differential algebras

Andrey Krutov, Pavle Pandžić (2024)

Archivum Mathematicum

Similarity:

We propose a definition of a quantised ${𝔰𝔩}_{2}$ -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of ${𝔰𝔩}_{2}$ are natural examples of such algebras.