We present diagrammatic schemes characterizing congruence 3-permutable and distributive algebras. We show that a congruence 3-permutable algebra is congruence meetsemidistributive if and only if it is distributive. We characterize varieties of algebras satisfying the so-called triangular scheme by means of a Maltsev-type condition.
@article{bwmeta1.element.doi-10_2478_BF02475233, author = {I. Chajda and R. Hala\v s}, title = {On schemes for congruence distributivity}, journal = {Open Mathematics}, volume = {2}, year = {2004}, pages = {368-376}, zbl = {1062.08002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475233} }
I. Chajda; R. Halaš. On schemes for congruence distributivity. Open Mathematics, Tome 2 (2004) pp. 368-376. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475233/
[1] I. Chajda: “A note on the triangular scheme”,East-West J. of Mathem., Vol. 3, (2001), pp. 79–80. | Zbl 1007.08002
[2] I. Chajda and E.K. Horváth: “A triangular scheme for congruence distributivity,”Acta Sci. Math. (Szeged), Vol. 68, (2002), pp. 29–35. | Zbl 0997.08001
[3] I. Chajda and E.K. Horváth: “A scheme for congruence semidistributivity”,Discuss. Math., General Algebra and Appl., Vol. 23, (2003), pp. 13–18. | Zbl 1057.08001
[4] I. Chajda, E.K. Horváth and G. Czédli: “Trapezoid Lemma and congruence distributivity”,Math. Slovaca, Vol. 53, (2003), pp. 247–253. | Zbl 1058.08007
[5] I. Chajda, E.K. Horváth and G. Czédli: “The Shifting Lemma and shifting lattice idetities”,Algebra Universalis, Vol. 50, (2003), pp. 51–60. http://dx.doi.org/10.1007/s00012-003-1808-2 | Zbl 1091.08006
[6] H.-P. Gumm: “Geometrical methods in congruence modular algebras”,Mem. Amer. Math. Soc., Vol. 45, (1983), pp. viii-79.
[7] B. Jónsson: “Algebras whose congruence lattices are distributive”,Math. Scand., Vol. 21, (1967), pp. 110–121. | Zbl 0167.28401