Related papers: A note on infinitely distributive inverse semigrou…

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.

This paper introduces a notion of presentation for locally inverse semigroups and develops a graph structure to describe the elements of locally inverse semigroups given by these presentations. These graphs will have a role similar to the…

Let $G$ be a connected reductive affine algebraic group defined over $\mathbb C$, and let $\Gamma$ be a cocompact lattice in $G$. We prove that any invariant bundle on $G/\Gamma$ is semistable.

An open problem in the theory of inverse semigroups was whether the variety of such semigroups, when viewed as algebras with a binary operation and a unary operation, is 2-based, that is, has a base for its identities consisting of 2…

Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…

We characterize the squares occurring in infinite overlap-free binary words and construct various alpha power-free binary words containing infinitely many overlaps.

We provide a unified approach, via deformations of incidence algebras, to several important types of representations with finiteness conditions, as well as the combinatorial algebras which produce them. We show that over finite dimensional…

In this paper we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly oredered associative ring on some specially defined subgroup concides with the composition of an inner…

We prove that every finite semigroup embeds in a finitely presented congruence-free monoid, and pose some questions around the Boone-Higman Conjecture.

We prove that the integral powers of the semicircular distribution are freely infinitely divisible. As a byproduct we get another proof of the free infnite divisibility of the classical Gaussian distribution.

Graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C*-algebras. This paper has two main goals: first, to provide an abstract characterization of graph inverse semigroups; and…

We consider random fields that can be represented as integrals of deterministic functions with respect to infinitely divisible random measures and show that these random fields are infinitely divisible.

We describe the additive subgroups of fields which are closed with respect to taking inverses. In particular, in characteristic different from two any such subgroup is either a subfield or the kernel of the trace map of a quadratic…

The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…

In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.

Word maps provide a wealth of information about finite groups. We examine the connection between the probability distribution induced by a word map and the underlying structure of a finite group. We show that a finite group is nilpotent if…

This paper gives a self-contained group-theoretic proof of a dual version of a theorem of Ore on distributive intervals of finite groups. We deduce a bridge between combinatorics and representations in finite group theory.

We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariant total order, and H is a locally nilpotent…

We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and…

A description of all subsemigroups of $M_2(\mathbb{C})$ which are given by a countable intersection of constructible sets is given. Furthermore, it is shown that they are intersections of constructible semigroups.