Balanced congruences

• Autorzy: Ivan Chajda , Günther Eigenthaler
• Języki publikacji: EN

Abstrakty

EN

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

EN

balanced congruence; balanced algebra; balanced variety; Mal'cev condition

Kategorie tematyczne

• 08B05: Equational logic, Mal\cprime cev (Mal\cprime tsev) conditions
• 08A30: Subalgebras, congruence relations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 105-114

Daty

wydano

2001

otrzymano

2000-03-27

poprawiono

2000-08-02

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40, CZ-77900 Olomouc, Czech Republic

autor

Günther Eigenthaler

• 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.

Identyfikatory

DOI

10.7151/dmgaa.1031