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On coatoms in lattices of quasivarieties of algebraic systems

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Abstract.

It is found the necessary condition for the lattice of quasivarieties has a finite set of coatoms. In particular if a quasivariety is generated by a finitely generated abelian-by-polycyclic-by-finite group or a totally ordered group then it has a finite set of proper maximal subquasivarieties. Also it is proved that the set of quasiverbal congruence relations of a finitely defined universal algebra is closed under any meets.

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Authors and Affiliations

  1. Altai State University, Dimitrova 66, 656099 Barnaul, Russia, e-mail: budkin@math.dcn-asu.ru, , , , , , RU

    A. I. Budkin

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  1. A. I. Budkin
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Received March 23, 1999; accepted in final form June 7, 1999.

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Budkin, A. On coatoms in lattices of quasivarieties of algebraic systems. Algebra univers. 46, 15–24 (2001). https://doi.org/10.1007/PL00022467

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  • DOI: https://doi.org/10.1007/PL00022467

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