Related papers: Total order compatible with addition on commutativ…

We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.

A discrete subset $S$ of a topological group $G$ is called a {\it suitable set} for $G$ if $S\cup \{e\}$ is closed in $G$ and the subgroup generated by $S$ is dense in $G$, where $e$ is the identity element of $G$. In this paper, the…

This paper has been withdrawn by the authors due to a crucial computational error. In this paper we deal with the finite case. We prove that a finite bounded ordered set can be represented as the order of principal congruences of a finite…

Let $\CaC\subset \Q^p$ be a rational cone. An affine semigroup $S\subset \CaC$ is a $\CaC$-semigroup whenever $(\CaC\setminus S)\cap \N^p$ has only a finite number of elements. In this work, we study the tree of $\CaC$-semigroups, give a…

We give a framework to produce constructible functions from natural functors between categories, without need of a morphism of moduli spaces to model the functor. We show using the Riemann-Hilbert correspondence that any natural (derived)…

In this paper, we state two combination theorems for relatively quasiconvex subgroups in a relatively hyperbolic group. Applications are given to the separability of double cosets of certain relatively quasiconvex subgroups and the…

In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a…

An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…

We prove the result in the title. We infer, that unlike cylindric algebras, there is a first order axiomatization of the class of completely representable polyadic algebras of infinite dimension, though the one we obtain is infinite; in…

It is shown that the Cuntz semigroup of a space with dimension at most two, and with second cohomology of its compact subsets equal to zero, is isomorphic to the ordered semigroup of lower semicontinuous functions on the space with values…

A semigroup $S$ is called an equational domain if any finite union of algebraic sets over $S$ is algebraic. We prove some necessary and sufficient conditions for a completely simple semigroup to be an equational domain.

We show that a lattice-ordered field (not necessarily commutative) is totally ordered if and only if each square is positive, answering a generalized question of Conrad and Dauns (Pacific J. Math. 30 (1969), 385--398) in the affirmative. As…

The aim of this paper is to generalize some fixed point theorems in the class of convex contraction of order $m$ on a complete suprametric space. Then, we will prove that the class of convex contraction of order m is strong enough to…

Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.

Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…

We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite…

We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main…

Let A be a subspace arrangement with a geometric lattice such that codim(x) > 1 for every x in A. Using rational homotopy theory, we prove that the complement M(A) is rationally elliptic if and only if the sum of the orthogonal subspaces is…

We show that, for every linear ordering of $[2]^n$, there is a large subcube on which the ordering is lexicographic. We use this to deduce that every long sequence contains a long monotone subsequence supported on an affine cube. More…

Let $\mathcal S$ be a set of monic degree $2$ polynomials over a finite field and let $C$ be the compositional semigroup generated by $\mathcal S$. In this paper we establish a necessary and sufficient condition for $C$ to be consisting…