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

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  • EP ID EP584881
  • DOI 10.15330/ms.51.1.3-11
  • Views 56
  • 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