Identities and Quasi-Identities of Pointed Algebras

A. O. Basheyeva; M. Mustafa; A. M. Nurakunov

doi:10.1134/S003744662202001X

Identities and Quasi-Identities of Pointed Algebras

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

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	197-205
Number of pages	9
Journal	Siberian Mathematical Journal
Volume	63
Issue number	2
DOIs	https://doi.org/10.1134/S003744662202001X
Publication status	Published - Mar 2022

Funding

The work was supported by Nazarbayev University FDCRG Grant no. 021220FD3851.

Keywords

512.57
finite axiomatizability
identity
pointed algebra
quasi-identity
quasivariety
variety

ASJC Scopus subject areas

General Mathematics

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10.1134/S003744662202001X

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title = "Identities and Quasi-Identities of Pointed Algebras",

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.",

keywords = "512.57, finite axiomatizability, identity, pointed algebra, quasi-identity, quasivariety, variety",

author = "Basheyeva, \{A. O.\} and M. Mustafa and Nurakunov, \{A. M.\}",

note = "Funding Information: The work was supported by Nazarbayev University FDCRG Grant no. 021220FD3851. Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = mar,

doi = "10.1134/S003744662202001X",

language = "English",

volume = "63",

pages = "197--205",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "Springer New York",

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TY - JOUR

T1 - Identities and Quasi-Identities of Pointed Algebras

AU - Basheyeva, A. O.

AU - Mustafa, M.

AU - Nurakunov, A. M.

PY - 2022/3

Y1 - 2022/3

N2 - 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.

AB - 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.

KW - 512.57

KW - finite axiomatizability

KW - identity

KW - pointed algebra

KW - quasi-identity

KW - quasivariety

KW - variety

UR - http://www.scopus.com/inward/record.url?scp=85127815209&partnerID=8YFLogxK

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U2 - 10.1134/S003744662202001X

DO - 10.1134/S003744662202001X

M3 - Article

AN - SCOPUS:85127815209

SN - 0037-4466

VL - 63

SP - 197

EP - 205

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

IS - 2

ER -

Identities and Quasi-Identities of Pointed Algebras

Abstract

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Keywords

ASJC Scopus subject areas

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