Ivan Chajda, Gerhard Dorfer, Helmut Länger (2004)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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We investigate some local versions of congruence permutability, regularity, uniformity and modularity. The results are applied to several examples including implication algebras, orthomodular lattices and relative pseudocomplemented lattices.
Ivan Chajda, Gábor Czédli, Eszter K. Horváth (2003)
Mathematica Slovaca
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Ivan Chajda, Branimir Šešelja, Andreja Tepavčević (2005)
Czechoslovak Mathematical Journal
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Some geometrical methods, the so called Triangular Schemes and Principles, are introduced and investigated for weak congruences of algebras. They are analogues of the corresponding notions for congruences. Particular versions of Triangular Schemes are equivalent to weak congruence modularity and to weak congruence distributivity. For algebras in congruence permutable varieties, stronger properties—Triangular Principles—are equivalent to weak congruence modularity and distributivity. ...
Ivan Chajda, Günther Eigenthaler (2001)
Discussiones Mathematicae - General Algebra and Applications
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It is well known that every congruence regular variety is n-permutable (in the sense of [9]) for some n ≥ 2. For the explicit proof see e.g. [2]. The connections between this n and Mal'cev type characterizations of congruence regularity were studied by G.D. Barbour and J.G. Raftery [1]. The concept of local congruence regularity was introduced in [3]. A common generalization of congruence regularity and local congruence regularity was given in [6] under the name "dual congruence regularity...