Work

A New Approach to Universal F-inverse Monoids in Enriched Signature

Year: 2024

Type: article

Abstract: We show that the universal X-generated F-inverse monoid F(G), where G is an X-generated group, introduced by Auinger, Szendrei and the first-named author, arises as a quotient inverse monoid of the Margolis-Meakin expansion $$M(G, X\cup {\overline{G}})$$ M ( G , X ∪ G ¯ ) of G, with respect to the extended generating set $$X\cup {\overline{G}}$$ X ∪ G ¯ , where $${\overline{G}}$$ G ¯ is a bijective copy of G which encodes the m-operation in F(G). The construction relies on a certain dual-closure operator on the semilattice of all finite and connected subgraphs containing the origin of the Cayley graph $${\text {Cay}}(G, X\cup {{\overline{G}}})$$ Cay ( G , X ∪ G ¯ ) and leads to a new and simpler proof of the universal property of F(G).

Source: Results in Mathematics

DOI: 10.1007/s00025-024-02291-4

Authors: Ganna Kudryavtseva, Ajda Lemut Furlani

Institutions: University of Ljubljana, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Javna Agencija za Raziskovalno Dejavnost RS