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In this letter we proved this theorem: \emph{if $F$ be a holomorphic mapping of $T_{\Omega}$ to a mapping manifold $X$ such that for every compact subset $K\subset \Omega$ the mapping $F$ is uniformly continues on $T_{K}$ and $F(T_{K})$ is…

This article studies the compatibility of Koenig's notion of an exact Borel subalgebra of a quasi-hereditary or, more generally, standardly stratified algebra with taking idempotent subalgebras or quotients. As an application, we provide…

It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…

The paper contains a description of the maximal ideal spaces (spectra) $\cM_A$ of bi-invariant function algebras $A$ on a compact group $G$. There are natural compatible structures in $\cM_A$: it is a compact topological semigroup with…

Much study has been done on semigroups which are unions of groups. There are several ways in which a union of groups can be made into a semigroup in which each of the component groups arises as subgroups of the constructed semigroup. An…

Let $\Lambda$ be an artin algebra and $\mathfrak{A}$ a two-sided idempotent ideal of $\Lambda$, that is, $\mathfrak{A}$ is the trace of a projective $\Lambda$-module $P$ in $\Lambda$. We consider the categories of finitely generated modules…

The aim of this paper is to introduce and study the class of all left braces in which every subbrace is an ideal. We call them Dedekind left braces. It is proved that every finite Dedekind left brace is centrally nilpotent. Structural…

We provide short and direct proofs for some classical theorems proved by Howie, Levi and McFadden concerning idempotent generated semigroups of transformations on a finite set.

We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…

Uninorms play a prominent role both in the theory and the applications of Aggregations and Fuzzy Logic. In this paper the class of group-like uninorms is introduced and characterized. First, two variants of a general construction -- called…

We give a classification of the principal and distinguished nilpotent pairs in all classical Lie algebras. As a classification of the principal pairs in the exceptional simple Lie algebras was obtained earlier (see Appendix to Ginzburg's…

An algorithm for the explicit computation of a complete set of primitive central idempotents, Wedderburn decomposition and the automorphism group of the semisimple group algebra of a finite metabelian group is developed. The algorithm is…

We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…

We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…

We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…

We develop a structure theory for nilpotent symplectic alternating algebras. We then give a classification of all nilpotent symplectic alternating algebras of dimension up to 10 over any field. The study reveals a new subclasses of powerful…

A topological group is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the group with its right uniformity is contained in an ambit. For n=0,1,2,..., every locally aleph_n bounded topological…

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…

A combing is a set of normal forms for a finitely generated group. This article investigates the language-theoretic and geometric properties of combings for nilpotent and polycyclic groups. It is shown that a finitely generated class 2…

We define a metric ultraproduct of topological groups with left-invariant metric, and show that there is a countable sequence of finite groups with left-invariant metric whose metric ultraproduct contains isometrically as a subgroup every…