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algebra universalis

, Volume 46, Issue 1–2, pp 15–24 | Cite as

On coatoms in lattices of quasivarieties of algebraic systems

  • A. I. Budkin

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.

Key words and phrases: Quasivariety, quasi-identity, lattice of quasivarieties, coatom. 

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Copyright information

© Birkhäuser Verlag Basel, 2001

Authors and Affiliations

  • A. I. Budkin
    • 1
  1. 1.Altai State University, Dimitrova 66, 656099 Barnaul, Russia, e-mail: budkin@math.dcn-asu.ruRU

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