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E-unitary and F-inverse monoids, and closure operators on group Cayley graphs.

Authors :
Szakács, N.
Source :
Acta Mathematica Hungarica. Jun2024, Vol. 173 Issue 1, p297-316. 20p.
Publication Year :
2024

Abstract

We show that the category of X-generated E-unitary inverse monoids with greatest group image G is equivalent to the category of G-invariant, finitary closure operators on the set of connected subgraphs of the Cayley graph of G. Analogously, we study F-inverse monoids in the extended signature (· , 1 , - 1 , m) , and show that the category of X-generated F-inverse monoids with greatest group image G is equivalent to the category of G-invariant, finitary closure operators on the set of all subgraphs of the Cayley graph of G. As an application, we show that presentations of F-inverse monoids in the extended signature can be studied by tools analogous to Stephen's procedure in inverse monoids, in particular, we introduce the notions of F-Schützenberger graphs and P-expansions. [ABSTRACT FROM AUTHOR]

Subjects

Subjects :
*CAYLEY graphs
*MONOIDS
*SUBGRAPHS

Details

Language :
English
ISSN :
02365294
Volume :
173
Issue :
1
Database :
Academic Search Index
Journal :
Acta Mathematica Hungarica
Publication Type :
Academic Journal
Accession number :
178415906
Full Text :
https://doi.org/10.1007/s10474-024-01443-w