Unified polynomials for congruence principality
Jaromír Duda (1987)
Mathematica Slovaca
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Jaromír Duda (1987)
Mathematica Slovaca
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Paweł Idziak (1999)
Banach Center Publications
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Ivan Chajda (2000)
Discussiones Mathematicae - General Algebra and Applications
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Varieties whose algebras have no idempotent element were characterized by B. Csákány by the property that no proper subalgebra of an algebra of such a variety is a congruence class. We simplify this result for permutable varieties and we give a local version of the theorem for varieties with nullary operations.
Hilda Draškovičová (1977)
Mathematica Slovaca
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Ivan Chajda, Jaromír Duda (1997)
Czechoslovak Mathematical Journal
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Dietmar Schweigert (1988)
Banach Center Publications
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Graham D. Barbour, James G. Raftery (1997)
Czechoslovak Mathematical Journal
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Don Pigozzi (1981)
Colloquium Mathematicae
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Ivan Chajda, Günther Eigenthaler (2001)
Discussiones Mathematicae - General Algebra and Applications
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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.