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Abstrakty
Let V be a variety with two distinct nullary operations 0 and 1. An algebra 𝔄 ∈ V is called balanced if for each Φ,Ψ ∈ Con(𝔄), we have [0]Φ = [0]Ψ if and only if [1]Φ = [1]Ψ. The variety V is called balanced if every 𝔄 ∈ V is balanced. In this paper, balanced varieties are characterized by a Mal'cev condition (Theorem 3). Furthermore, some special results are given for varieties of bounded lattices.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
105-114
Opis fizyczny
Daty
wydano
2001
otrzymano
2000-03-27
poprawiono
2000-08-02
Twórcy
autor
- Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40, CZ-77900 Olomouc, Czech Republic
autor
- Institut für Algebra und Computermathematik, Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
Bibliografia
- [1] I. Chajda, Locally regular varieties, Acta Sci. Math. (Szeged) 64 (1998), 431-435.
- [2] I. Chajda and G. Eigenthaler, A remark on congruence kernels in complemented lattices and pseudocomplemented semilattices, Contributions to General Algebra 11 (1999), 55-58.
- [3] G. Grätzer and E.T. Schmidt, Ideals and congruence relations in lattices, Acta Math. Sci. Hungar. 9 (1958), 137-175.
- [4] A.I. Mal'cev, On the general theory of algebraic systems (Russian), Mat. Sb. 35 (1954), 3-20.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1031