Balanced congruences

Ivan Chajda; Günther Eigenthaler

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 1, page 105-114
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Ivan Chajda, and Günther Eigenthaler. "Balanced congruences." Discussiones Mathematicae - General Algebra and Applications 21.1 (2001): 105-114. <http://eudml.org/doc/287615>.

@article{IvanChajda2001,
abstract = {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.},
author = {Ivan Chajda, Günther Eigenthaler},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {balanced congruence; balanced algebra; balanced variety; Mal'cev condition; Mal'tsev condition},
language = {eng},
number = {1},
pages = {105-114},
title = {Balanced congruences},
url = {http://eudml.org/doc/287615},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Ivan Chajda
AU - Günther Eigenthaler
TI - Balanced congruences
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 1
SP - 105
EP - 114
AB - 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.
LA - eng
KW - balanced congruence; balanced algebra; balanced variety; Mal'cev condition; Mal'tsev condition
UR - http://eudml.org/doc/287615
ER -

References

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  1. [1] I. Chajda, Locally regular varieties, Acta Sci. Math. (Szeged) 64 (1998), 431-435. 
  2. [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. Zbl0940.06009
  3. [3] G. Grätzer and E.T. Schmidt, Ideals and congruence relations in lattices, Acta Math. Sci. Hungar. 9 (1958), 137-175. Zbl0085.02002
  4. [4] A.I. Mal'cev, On the general theory of algebraic systems (Russian), Mat. Sb. 35 (1954), 3-20. 

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