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
- EP ID EP584881
- DOI 10.15330/ms.51.1.3-11
- Views 52
- Downloads 0
The Fourier problem for weakly nonlinear integro-differential elliptic-parabolic systems
The Fourier problem or, in other words, the problem without initial conditions for weakly nonlinear elliptic-parabolic systems are considered in this paper. The existence and uniqueness solutions of the problem are prove...
Approximation of periodic analytic functions by Fejer sums
For upper bounds of the deviations of Fejer sums taken over classes of periodic functions that admit analytic extensions to a fixed strip of the complex plane, we obtain asymptotic equalities. In certain cases, these equ...
Polynomial complex Ginzburg-Landau equations in Zhidkov spaces
We consider the so-called Complex Ginzburg-Landau equations with a polynomial nonlin- earity in the real line. We prove existence results concerned with the initial value problem for these equations in Zhidkov spaces wit...
The analogue of Bernstein’s inverse theorem for the one class of the space of sequences (in Ukrainian)
We introduce the space of numerical sequences lp={x=(ξk)∞k=1:|x|=∑∞k=1|ξk|pk≤+∞} with a quasi-norm |⋅| for an every sequence p=(pk)∞k=1 of numbers pk from the interval (0,1] and we prove the analogue of the inverse of Be...
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.