The word problem for $$\kappa $$-terms over the pseudovariety of local groups

Autor:	M. L. Teixeira, José Carlos Costa, Conceição Nogueira
Rok vydání:	2021
Předmět:	Combinatorics Mathematics::Logic Algebra and Number Theory Canonical form Word problem (mathematics) Basis (universal algebra) Algebra over a field Variety (universal algebra) Signature (topology) Kappa Mathematics
Zdroj:	Semigroup Forum. 103:439-468
ISSN:	1432-2137 0037-1912
DOI:	10.1007/s00233-021-10207-9
Popis:	In this paper we study the $$\kappa $$ -word problem for the pseudovariety $$\mathbf{LG}$$ of local groups, where $$\kappa $$ is the canonical signature consisting of the multiplication and the pseudoinversion. We solve this problem by transforming each arbitrary $$\kappa $$ -term $$\alpha $$ into another one $$\alpha ^*$$ called the $$\mathbf{LG}$$ -canonical form of $$\alpha $$ and by showing that different canonical forms have different interpretations over $$\mathbf{LG}$$ . The procedure of construction of these canonical forms consists in applying reductions determined by a set $$\Sigma $$ of $$\kappa $$ -identities. As a consequence, $$\Sigma $$ is a basis of $$\kappa $$ -identities for the $$\kappa $$ -variety generated by $$\mathbf{LG}$$ .
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4764e7bdbe5a5d6ec003ecc0ac4d44e0 https://doi.org/10.1007/s00233-021-10207-9 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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