Identities and Quasi-Identities of Pointed Algebras

A. O. Basheyeva, Manat Mustafa, Anvar M. Nurakunov

2022

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DOI 10.1134/s003744662202001x
Data confidence 70 medium
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Abstract

Each pointed enrichment of an algebra can be regarded as the same algebra with an additional finite set of constant operations. An algebra is pointed whenever it is a pointed enrichment of some algebra. We show that each pointed enrichment of a finite algebra in a finitely axiomatizable residually very finite variety admits a finite basis of identities. We also prove that every pointed enrichment of a finite algebra in a directly representable quasivariety admits a finite basis of quasi-identities. We give some applications of these results and examples.