Abstract
The present work considers algebras and their enrichments. It is shown by two examples of finite lattices that the properties “to have (no) a finite basis of quasi-identities” and “to generate a standard topological quasivariety” are not preserved with respect to pointed enrichments of finite algebras.
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Acknowledgements
The research was carried out while the third author was visiting the Department of Mathematics of Nazarbayev University, Nur-Sultan. The authors thank Nazarbayev University for its warm hospitality. The authors are grateful for referee to his(her) for constructive comments and suggestions that allowed to improve this manuscript.
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Presented by R. Willard.
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The work was supported by Nazarbayev University Faculty Development Competitive Research Grants N090118FD5342. The first and the third authors were partially supported by MES RK grant No AP09258863 “Selected problems of universal algebra and lattice theory”.
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Basheyeva, A.O., Mustafa, M. & Nurakunov, A.M. Properties not retained by pointed enrichments of finite lattices. Algebra Univers. 81, 56 (2020). https://doi.org/10.1007/s00012-020-00692-4
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DOI: https://doi.org/10.1007/s00012-020-00692-4