Related papers: Monoids with absorbing elements and their associat…
An additive submonoid of the nonnegative cone of the real line is called a positive monoid. Positive monoids consisting of rational numbers (also known as Puiseux monoids) have been the subject of several recent papers. Moreover, those…
We study endomorphisms and derivations of infinite dimensional cyclic Leibniz algebra.
This article contains an overview of the results of the author in a field of algebraic topology used in computer science. The relationship between the cubical homology groups of generalized tori and homology groups of partial trace monoid…
Geometric properties of schemes obtained by gluing algebras of monoids, including separation and finiteness properties, irreducibility, normality, catenarity, dimension, and Serre's properties (S_k) and (R_k), are investigated. This is used…
The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.
An objective of the theory of combinatorial groupoids is to introduce concepts like "holonomy", "parallel transport", "bundles", "combinatorial curvature" etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes,…
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine…
The work starts a series of papers on topological radicals and their applications. Among other results we present a theory of radicals related to the joint tensor radius.
This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…
The primary contribution of this thesis is to introduce and examine the planar modular partition monoid for parameters $m, k \in \mathbb{Z}_{>0}$, which has simultaneously and independently generated interest from other researchers as…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
Combinatorial Hopf algebras arise in a variety of applications. Recently, Aguiar and Mahajan showed how many well-studied Hopf algebras are closely related to Hopf monoids in species. In this paper, we study Hopf monoids in graphical…
Extending Eilenberg-Mac Lane's methods, higher level cohomologies for commutative monoids are introduced and studied. Relationships with pre-existing theories (Leech, Grillet, ...) are stated. The paper includes a cohomological…
This article explains basic constructions and results on group algebras and their cohomology, starting from the point of view of commutative algebra. It provides the background necessary for a novice in this subject to begin reading Dave…
Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.
In this paper, we consider the monoids of all partial endomorphisms, of all partial weak endomorphisms, of all injective partial endomorphisms, of all partial strong endomorphisms and of all partial strong weak endomorphisms of a star graph…
The use of the properties of actions on an algebra to enrich the study of the algebra is well-trodden and still fashionable. Here, the notion and study of endomorphic elements of (Banach) algebras are introduced. This study is initiated, in…
The stationary problem of light interaction with a dense collection of two-level atoms embedded in a dielectric is treated semiclassically. The effect of dielectric absorption on the phenomenon of intrinsic optical bistability is discussed…