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E-unitary and F-inverse monoids, and closure operators on group Cayley graphs.
- 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 :
- *CAYLEY graphs
*MONOIDS
*SUBGRAPHS
Subjects
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