Finite atomistic lattices that can be represented as lattices of quasivarieties

• Autorzy: K. V. Adaricheva , Wiesław Dziobiak , V. A. Gorbunov
• Języki publikacji: EN

Abstrakty

EN

We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].

Słowa kluczowe

EN

atomistic lattice; quasivariety; Mal'cev problem; equa-closure operator; semilattice

Kategorie tematyczne

• 06B15: Representation theory
• 03C99: None of the above, but in this section
• 08A99: None of the above, but in this section
• 08C15: Quasivarieties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1993
• Tom: 142
• Numer: 1
• Strony: 19-43

Daty

wydano

1993

otrzymano

1991-05-20

poprawiono

1992-03-03

Twórcy

autor

K. V. Adaricheva

• Institute of Mathematics, Russian Academy of Sciences, Universitetskiĭ Prosp. 4, 630090 Novosibirsk, Russia

autor

Wiesław Dziobiak

• Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

autor

V. A. Gorbunov

• Institute of Mathematics, Russian Academy of Sciences, Universitetskiĭ Prosp. 4, 630090 Novosibirsk, Russia

Bibliografia

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• [11] V. A. Gorbunov and V. I. Tumanov, A class of lattices of quasivarieties, ibid. 19 (1980), 59-80 (in Russian).
• [12] V. A. Gorbunov and V. I. Tumanov, The structure of the lattices of quasivarieties, in: Trudy Inst. Mat. (Novosibirsk) 2, Nauka Sibirsk. Otdel., Novosibirsk 1982, 12-44 (in Russian).
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• [17] A. I. Mal'cev, Algebraic Systems, Springer, 1973.
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