Varieties satisfying the triangular scheme need not be congruence distributive
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2007)
- Volume: 46, Issue: 1, page 19-24
- ISSN: 0231-9721
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topChajda, Ivan, and Halaš, Radomír. "Varieties satisfying the triangular scheme need not be congruence distributive." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 46.1 (2007): 19-24. <http://eudml.org/doc/32456>.
@article{Chajda2007,
abstract = {A diagrammatic scheme characterizing congruence distributivity of congruence permutable algebras was introduced by the first author in 2001. It is known under the name Triangular Scheme. It is known that every congruence distributive algebra satisfies this scheme and an algebra satisfying the Triangular Scheme which is not congruence distributive was found by E. K. Horváth, G. Czédli and the autor in 2003. On the other hand, it was an open problem if a variety of algebras satisfying the Triangular Scheme must be congruence distributive. We get a negative solution by presenting an example.},
author = {Chajda, Ivan, Halaš, Radomír},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {congruence distributivity; Triangular Scheme; variety of algebras; Jónsson terms; congruence; Triangular Scheme; congruence distributive; congruence permutable; variety; Mal'tsev condition},
language = {eng},
number = {1},
pages = {19-24},
publisher = {Palacký University Olomouc},
title = {Varieties satisfying the triangular scheme need not be congruence distributive},
url = {http://eudml.org/doc/32456},
volume = {46},
year = {2007},
}
TY - JOUR
AU - Chajda, Ivan
AU - Halaš, Radomír
TI - Varieties satisfying the triangular scheme need not be congruence distributive
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2007
PB - Palacký University Olomouc
VL - 46
IS - 1
SP - 19
EP - 24
AB - A diagrammatic scheme characterizing congruence distributivity of congruence permutable algebras was introduced by the first author in 2001. It is known under the name Triangular Scheme. It is known that every congruence distributive algebra satisfies this scheme and an algebra satisfying the Triangular Scheme which is not congruence distributive was found by E. K. Horváth, G. Czédli and the autor in 2003. On the other hand, it was an open problem if a variety of algebras satisfying the Triangular Scheme must be congruence distributive. We get a negative solution by presenting an example.
LA - eng
KW - congruence distributivity; Triangular Scheme; variety of algebras; Jónsson terms; congruence; Triangular Scheme; congruence distributive; congruence permutable; variety; Mal'tsev condition
UR - http://eudml.org/doc/32456
ER -
References
top- Chajda I., A note on the triangular scheme, East-West J. of Mathem. 3 (2001), 79–80. Zbl1007.08002MR1866645
- Chajda I., Halaš R., On schemes for congruence distributivity, , Central European J. of Mathem. 2, 3 (2004), 368–376. Zbl1062.08002MR2113537
- Chajda I., Horváth E. K., A scheme for congruence semidistributivity, Discuss. Math., General Algebra and Appl. 23 (2003), 13–18. Zbl1057.08001MR2070042
- Chajda I., Horváth E. K., A triangular scheme for congruence distributivity, Acta Sci. Math. (Szeged) 68 (2002), 29–35. Zbl0997.08001MR1916565
- Chajda I., Horváth E. K., Czédli G., Trapezoid Lemma and congruence distributivity, Math. Slovaca 53 (2003), 247–253. Zbl1058.08007MR2025021
- Chajda I., Horváth E. K., Czédli G., The Shifting Lemma and shifting lattice identities, Algebra Universalis 50 (2003), 51–60. Zbl1091.08006MR2026826
- Jónsson B., Algebras whose congruence lattice are distributive, Math. Scand. 21 (1967), 110–121. (1967) MR0237402
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