Identities and Quasi-Identities of Pointed Algebras

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

Research output: Contribution to journalArticlepeer-review

Abstract

Each pointed enrichment of an algebra can be regarded asthe 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 algebrain a finitely axiomatizable residually very finite variety admits a finite basis of identities.We also prove thatevery pointed enrichment of a finite algebrain a directly representable quasivarietyadmits a finite basis of quasi-identities.We give some applications of these results and examples.

Original languageEnglish
Pages (from-to)197-205
Number of pages9
JournalSiberian Mathematical Journal
Volume63
Issue number2
DOIs
Publication statusPublished - Mar 2022

Keywords

  • 512.57
  • finite axiomatizability
  • identity
  • pointed algebra
  • quasi-identity
  • quasivariety
  • variety

ASJC Scopus subject areas

  • Mathematics(all)

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