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
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