Related papers: On absorption in semigroups and $n$-ary semigroups
Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the…
We introduce the new notion of quotient-saturation as a measure of the immensity of the quotient structure of a group. We present a sufficient condition for a finitely presented group to be quotient-saturated, and use it to deduce that…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
Let $A$ be a simple infinite dimensional stably finite unital C*-algebra, and let $B$ be a centrally large subalgebra of $A$. We prove that if $A$ is tracially ${\mathcal{Z}}$-absorbing if and only if $B$ is tracially…
The derivation of absorber theory is outlined in very detail. Absorber theory is based on classical action-at-a-distance electrodynamics, but it deviates from that theory at a crucial point. It is shown that (a) absorber theory cannot…
We exhibit a simple condition under which a finite involutary semigroup whose semigroup reduct is inherently nonfinitely based is also inherently nonfinitely based as a unary semigroup. As applications, we get already known as well as new…
A finite group is called semi-rational if the distribution induced on it by any word map is a virtual character. Amit and Vishne give a sufficient condition for a group to be semi-rational, and ask whether it is also necessary. We answer…
Ideal absorption describes a particular means of optimizing light-matter interactions with a host of potential applications. This work presents new analytic formulas and describes semi-analytical methods for the design of electric or…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
A new type of semigroups which appears while dealing with $N=1$ superconformal symmetry in superstring theories is considered. The ideal series having unusual abstract properties is constructed. Various idealisers are introduced and…
Let $G$ be a group with identity $e$, $R$ be a commutative $G$-graded ring with unity $1$ and $M$ be a $G$-graded unital $R$-module. In this article, we introduce the concept of graded $1$-absorbing prime submodule. A proper graded…
Absorbing boundaries are frequently employed in real-time propagation of the Schr\"odinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an…
A general mechanism for "breaking" commutativity in algebras is proposed: if the underlying set is taken to be not a crisp set, but rather an obscure/fuzzy set, the membership function, reflecting the degree of truth that an element belongs…
We consider the notion of strong self-absorption for continuous actions of locally compact groups on the hyperfinite II$_1$-factor and characterize when such an action is tensorially absorbed by another given action on any separably acting…
A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the $d$-dimensional Euclidean space with $d\geq 2$. Spheres arrive sequentially at…
In this paper, we introduce some classes of generalized tracial approximation ${\rm C^*}$-algebras. Consider the class of unital ${\rm C^*}$-algebras which are tracially $\mathcal{Z}$-absorbing (or have tracial nuclear dimension at most…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
The theory of abelian categories proved very useful, providing an axiomatic framework for homology and cohomology of modules over a ring and, in particular, of abelian groups. For many years, a similar categorical framework has been lacking…
We present a non-uniform analogue of the classical Datko-Pazy theorem. Our main result shows that an integrability condition imposed on orbits originating in a fractional domain of the generator (as opposed to all orbits) implies polynomial…
We study an explicit description of semibricks and 2-term simple-minded collections over preprojective algebras of type $A$ via arc diagrams. We provide a bijection between the set of noncrossoing arc diagrams (resp. the set of double arc…