An alternative look at the structure of graph inverse semigroups

Journal Title: Математичні Студії - Year 2019, Vol 51, Issue 1

Abstract

For any graph inverse semigroup G(E) we describe subsemigroups D0=D∪{0} and J0=J∪{0} of G(E) where D and J are arbitrary D-class and J-class of G(E), respectively. In particular, we prove that for each D-class D of a graph inverse semigroup over an acyclic graph the semigroup D0 is isomorphic to a semigroup of matrix units. Also we show that for any elements a,b of a graph inverse semigroup G(E), Ja⋅Jb∪Jb⋅Ja⊂J0b if there exists a path w such that s(w)∈Ja and r(w)∈Jb.

Authors and Affiliations

S. Bardyla

Keywords

Related Articles

Convergence analysis of the Gauss-Newton- Potra method for nonlinear least squares problems

In this paper we study an iterative differential-difference method for solving nonlinear least squares problems with nondifferentiable residual function. We have proved theorems which establish the conditions of converge...

Linear expand-contract plasticity of ellipsoids in separable Hilbert spaces

The paper is aimed to establish the interdependence between linear expand-contract plasticity of an ellipsoid in a separable Hilbert spaces and properties of the set of its semi-axes.

Matrix representation of Taylor’s formula for mappings in finite dimensional spaces

In this paper, the matrix representations of derivatives, differentials and Taylor’s formulas for functionals and mappings are presented. The behavior law of intermediate points in the formula’s remainder terms is found...

Geometric relations in an arbitrary metric space

The paper is devoted to individual elements of metric geometry. Analytical relations are considered that concern the distances between points of a metric space and have a definite geometric interpretation. These relation...

On applications of the Levi method in the theory of parabolic equations

A short review of papers where a fundamental solution was constructed by the Levi’s parametrix method is done. Some details of applications of this method for parabolic equations and systems of parabolic equations, in pa...

Download PDF file
  • EP ID EP584881
  • DOI 10.15330/ms.51.1.3-11
  • Views 55
  • Downloads 0

How To Cite

S. Bardyla (2019). An alternative look at the structure of graph inverse semigroups. Математичні Студії, 51(1), 3-11. https://europub.co.uk/articles/-A-584881