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 |
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Pages (from-to) | 197-205 |
Number of pages | 9 |
Journal | Siberian Mathematical Journal |
Volume | 63 |
Issue number | 2 |
DOIs | |
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