Direct product decompositions of directed groups
Ján Jakubík (1989)
Czechoslovak Mathematical Journal
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Ján Jakubík (1989)
Czechoslovak Mathematical Journal
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Manfred Armbrust (1973)
Colloquium Mathematicae
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Marica D. Prešić (1979)
Publications de l'Institut Mathématique
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Magill, K.D.jun. (1984)
International Journal of Mathematics and Mathematical Sciences
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Krisztina Balog, Benedek Skublics (2011)
Discussiones Mathematicae - General Algebra and Applications
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We define the order-congruence distributivity at 0 and order- congruence n-distributivity at 0 of ordered algebras with a nullary operation 0. These notions are generalizations of congruence distributivity and congruence n-distributivity. We prove that a class of ordered algebras with a nullary operation 0 closed under taking subalgebras and direct products is order-congruence distributive at 0 iff it is order-congruence n-distributive at 0. We also characterize such classes by a Mal'tsev...
Scott Ahlgren (2003)
Acta Arithmetica
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Hao Pan (2007)
Acta Arithmetica
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Ivan Chajda, Radomír Halaš (2002)
Discussiones Mathematicae - General Algebra and Applications
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We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.
Ying Zhang (2007)
Acta Arithmetica
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Ivan Chajda, Václav Snášel (1998)
Mathematica Bohemica
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A concept of congruence preserving upper and lower bounds in a poset is introduced. If is a lattice, this concept coincides with the notion of lattice congruence.