Related papers: Weak Sequential Completeness of Uniform Algebras

We prove that if $B\subseteq A$ is an extension of finite dimensional algebras such that the projective dimension of $A/B$ as a $B$-bimodule is finite, if $A$ has finite finitistic dimension, then so does $B$. We exhibit examples…

The weak Whyburn property is a generalization of the classical sequential property that has been studied by many authors. A space $X$ is weakly Whyburn if for every non-closed set $A \subset X$ there is a subset $B \subset A$ such that…

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

We generalize the notion of an exact category and introduce weakly exact categories. A proof of the snake lemma in this general setting is given. Some applications are given to illustrate how one can do homological algebra in a weakly exact…

We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…

We study the metric dimension (strong and weak) of infinite graphs. In particular, our main interest is characterizing infinite graphs with finite dimension. Our main results: (1) graphs with more than one end have infinite strong…

We study equations over boolean algebras with distinguished elements. We prove the criteria, when a boolean algebra is equationally Noetherian, weakly equationally Noetherian, $\mathbf{q}_\omega$-compact or $\mathbf{u}_\omega$-compact. Also…

We consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. There is substantial confusion in the literature if one tries to describe all the non-equivalent deformations of a given Lie algebra.…

Suppose A is a unital subhomogeneous C*-algebra. We show that every central sequence in A is hypercentral if and only if every pointwise limit of a sequence of irreducible representations is multiplicity free. We also show that every…

Algebra bundles, in the strict sense, appear in many areas of geometry and physics. However, the structure of an algebra is flexible enough to vary non-trivially over a connected base, giving rise to a structure of a weak algebra bundle. We…

The notion of weak tiling played a key role in the proof of Fuglede's spectral set conjecture for convex domains, due to the fact that every spectral set must weakly tile its complement. In this paper, we revisit the notion of weak tiling…

For representation by partial functions in the signature with intersection, composition and antidomain, we show that a representation is meet complete if and only if it is join complete. We show that a representation is complete if and only…

Let $A$ be a Banach algebra. For $f\in A^{\ast}$, we inspect the weak sequential properties of the well-known map $T_f:A\to A^{\ast}$, $T_f(a) = fa$, where $fa\in A^{\ast}$ is defined by $fa(x) = f(ax)$ for all $x\in A$. We provide…

We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure $M$. We prove that if $T$ is a complete $L$-theory, then $T$ is mutually algebraic if and only if there is some model $M$ of $T$ for…

Let $\mathbb F$ be an algebraically closed field, $G$ be an abelian group, and let $A$ and $B$ be arbitrary finite-dimensional $G$-graded simple algebras over $\mathbb F$. We prove that $A$ and $B$ are isomorphic if, and only if, they…

Let A,B be finite dimensional G-graded algebras over an algebraically closed field K with char(K)=0, where G is an abelian group, and let Id_G(A) be the set of graded identities of A (res. Id_G(B)). We show that if A,B are G-simple then…

Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…

In this paper we introduce {\em weak ascent sequences}, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the following objects: permutations avoiding a particular…

Our (weak) conjecture claims that a finite dimensional Lie algebra ${\bf g}$ over the field of complex numbers is semi-simple iff the Leibniz homology vanishes in positive dimensions $HL_i({\bf g})=0$, $i>0$. We will indicate a mistake in…

We study universal enveloping Hopf algebras of Lie algebras in the category of weakly complete vector spaces over the real and complex field.