相关论文: On quasi-separative semigroups
We introduce a preorder on an inverse semigroup $S$ associated to any normal inverse subsemigroup $N$, that lies between the natural partial order and Green's ${\mathscr J}$-relation. The corresponding equivalence relation $\simeq_N$ is not…
We prove several congruences for trinomial coefficients.
We construct quasi-isometry invariants of a one-ended finitely presented group by considering the tree of cylinders of a two-ended JSJ decomposition of the group. When the group satisfies additional quasi-isometric rigidity hypotheses we…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
We prove that any quasigroup admissing complete or quasicomplete mapping has a prolongation to a quasigroup having one element more.
In this paper we give an algebraic characterization of assemblies in terms of bands of groups. We also consider substructures and homomorphisms of assemblies. We give many examples and counterexamples.
We study congruences on the partial automorphism monoid of a finite rank free group action. We give a decomposition of a congruence on this monoid into a Rees congruence, a congruence on a Brandt semigroup and an idempotent separating…
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 binary products of right, left or double division in semigroups that are semilattices of groups give interesting groupoid structures that are in one to one correspondence with semigroups that are semilattices of groups. This work is…
Given a connected linear algebraic group $G$, we descrive the subgroup of $G$ generated by all semisimple elements.
We initiate a study of E-semigroups over convex cones. We prove a structure theorem for E-semigroups which leave the algebra of compact operators invariant. Then we study in detail the CCR flows, E$_0$semigroups constructed from isometric…
We define quasi-Frobenius semigroups and find necessary and sufficient conditions under which a semigroup algebra of a 0-cancellative semigroup is quasi-Frobenius.
Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…
Given a $\Gamma$-semigroup $S$, we construct a semigroup $\Sigma$ in such a way that one sided ideals and quasi-ideals of $S$ can be regarded as one sided ideals and quasi-ideals respectively of $\Sigma$. This correspondence and other…
For a group $G$, we construct a quasi morphism from its left orderings and the map from the space of left orderings to the second bounded cohomology. We show that these maps reflect various properties of the group orderings.
Congruences on a graph inverse semigroup were recently described in terms of the underline graph. Based on such descriptions, we show that the lattice of congruences on a graph inverse semigroup is upper semimodular but not lower…
We study almost symmetric numerical semigroups and semigroup rings. We describe a characteristic property of the minimal free resolution of the semigroup ring of an almost symmetric numerical semigroup. For almost symmetric semigroups…
This is the first of two papers which aim to understand quasi-isometries of a subclass of unimodular split solvable Lie groups. In the present paper, we show that locally (in a coarse sense), a quasi-isometry between two groups in this…
The paper deals with quasigroups having a trivial group of automorphisms and a trivial group of autotopisms. Examples of such quasigroups and methods of their verification are given.
We construct a family of representations of an arbitrary variant $S_a$ of a semigroup $S$, induced by a given representation of $S$, and investigate properties of such representations and their kernels.