Related papers: On disjunctions of equations over semigroups
Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. In this paper we will consider the special case where all division rings are…
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.
Since its introduction by Symons, the semigroup of maps with restricted range has been studied in the context of transformations on a set, or of linear maps on a vector space. Sets and vector spaces being particular examples of independence…
A group $G$ is integrable if it is isomorphic to the derived subgroup of a group $H$; that is, if $H'\simeq G$, and in this case $H$ is an integral of $G$. If $G$ is a subgroup of $U$, we say that $G$ is integrable within $U$ if $G=H'$ for…
We prove that the problems of representing a finite ordered complemented semigroup or finite lattice-ordered semigroup as an algebra of binary relations over a finite set are undecidable. In the case that complementation is taken with…
A group $G$ is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of $G$, there exists a finite quotient of $G$ where the images of these subgroups are not conjugate. We prove that limit…
Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary.
A natural operation on numerical semigroups is taking a quotient by a positive integer. If $\mathcal S$ is a quotient of a numerical semigroup with $k$ generators, we call $\mathcal S$ a $k$-quotient. We give a necessary condition for a…
This paper considers numerical semigroups $S$ that have a non-principal relative ideal $I$ such that $\mu_S(I)\mu_S(S-I)=\mu_S(I+(S-I)) $. We show the existence of an infinite family of such which $I+(S-I)=S\backslash\{0\}$. We also show…
A sumset semigroup is a non-cancellative commutative monoid obtained from the sumset of finite non-negative integer sets. In this work, an algorithm for computing the ideals associated with some sumset semigroups is provided. Using these…
Profinite semigroups are a generalization of finite semigroups that come about naturally when one is interested in considering free structures with respect to classes of finite semigroups. They also appear naturally through dualization of…
We call an affine algebraic supergroup quasireductive if its underlying algebraic group is reductive. We obtain some results about the structure and representations of reductive supergroups.
Dickson's commutative semifields are an important class of finite division algebras. We generalise Dickson's construction of commutative division algebras by doubling both finite field extensions and central simple algebras and not…
We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…
First of all, we recall the well known notion of semidirect product both for classical algebraic structures (like groups and rings) and for more recent ones (digroups, left skew braces, heaps, trusses). Then we analyse the concept of…
An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical. Such a semi-reductive algebraic group naturally arises and also plays a key role in the study of modular…
Elements $a,b$ of a semigroup $S$ are said to be \emph{primarily conjugate} or just \emph{p-conjugate}, if there exist $x,y\in S^1$ such that $a=xy$ and $b=yx$. The p-conjugacy relation generalizes conjugacy in groups, but for general…
A numerical semigroup is an additive subsemigroup of the natural numbers that contains zero and has finite complement. A numerical semigroup is irreducible if it cannot be written as an intersection of numerical semigroups properly…
The notion of automatic selfadjointness of all ideals in a multiplicative semigroup of the bounded linear operators on a separable Hilbert space B(H) arose in a 2015 discussion with Heydar Radjavi who pointed out that B(H) and the finite…
Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called (1) $\mathcal C$-$closed$ if $X$ is closed in every topological semigroup $Y\in\mathcal C$ containing $X$ as a discrete subsemigroup, (2) $ideally$ $\mathcal…