The word problem for κ-terms over the pseudovariety of local groups

Costa, J. C.; Nogueira, C.; Teixeira, M. L.

http://hdl.handle.net/10400.8/15423

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The word problem for κ-terms over the pseudovariety of local groups.pdf	In this paper we study the κ-word problem for the pseudovariety LG of local groups, where κ is the canonical signature consisting of the multiplication and the pseudoinversion. We solve this problem by transforming each arbitrary κ-term α into another one α∗ called the LG-canonical form of α and by showing that different canonical forms have different interpretations over LG. The procedure of construction of these canonical forms consists in applying reductions determined by a set Σ of κ-identities. As a consequence, Σ is a basis of κ-identities for the κ-variety generated by LG.	446.15 KB	Adobe PDF	Ver/Abrir

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Autores

Costa, J. C.

Nogueira, C.

Teixeira, M. L.

Resumo(s)

In this paper we study the κ-word problem for the pseudovariety LG of local groups, where κ is the canonical signature consisting of the multiplication and the pseudoinversion. We solve this problem by transforming each arbitrary κ-term α into another one α∗ called the LG-canonical form of α and by showing that different canonical forms have different interpretations over LG. The procedure of construction of these canonical forms consists in applying reductions determined by a set Σ of κ-identities. As a consequence, Σ is a basis of κ-identities for the κ-variety generated by LG.

Palavras-chave

Local group Pseudovariety Finite semigroup Implicit signature Word problem κ-term Canonical form

URI

http://hdl.handle.net/10400.8/15423

Citação

Costa, J.C., Nogueira, C. & Teixeira, M.L. The word problem for k-terms over the pseudovariety of local groups. Semigroup Forum 103, 439–468 (2021). https://doi.org/10.1007/s00233-021-10207-9.