On schemes for congruence distributivity

I. Chajda; R. Halaš

Open Mathematics (2004)

  • Volume: 2, Issue: 3, page 368-376
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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I. Chajda, and R. Halaš. "On schemes for congruence distributivity." Open Mathematics 2.3 (2004): 368-376. <http://eudml.org/doc/268712>.

@article{I2004,
abstract = {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.},
author = {I. Chajda, R. Halaš},
journal = {Open Mathematics},
keywords = {08A30; 08B10; 08B05},
language = {eng},
number = {3},
pages = {368-376},
title = {On schemes for congruence distributivity},
url = {http://eudml.org/doc/268712},
volume = {2},
year = {2004},
}

TY - JOUR
AU - I. Chajda
AU - R. Halaš
TI - On schemes for congruence distributivity
JO - Open Mathematics
PY - 2004
VL - 2
IS - 3
SP - 368
EP - 376
AB - 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.
LA - eng
KW - 08A30; 08B10; 08B05
UR - http://eudml.org/doc/268712
ER -

References

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  1. [1] I. Chajda: “A note on the triangular scheme”,East-West J. of Mathem., Vol. 3, (2001), pp. 79–80. Zbl1007.08002
  2. [2] I. Chajda and E.K. Horváth: “A triangular scheme for congruence distributivity,”Acta Sci. Math. (Szeged), Vol. 68, (2002), pp. 29–35. Zbl0997.08001
  3. [3] I. Chajda and E.K. Horváth: “A scheme for congruence semidistributivity”,Discuss. Math., General Algebra and Appl., Vol. 23, (2003), pp. 13–18. Zbl1057.08001
  4. [4] I. Chajda, E.K. Horváth and G. Czédli: “Trapezoid Lemma and congruence distributivity”,Math. Slovaca, Vol. 53, (2003), pp. 247–253. Zbl1058.08007
  5. [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 Zbl1091.08006
  6. [6] H.-P. Gumm: “Geometrical methods in congruence modular algebras”,Mem. Amer. Math. Soc., Vol. 45, (1983), pp. viii-79. 
  7. [7] B. Jónsson: “Algebras whose congruence lattices are distributive”,Math. Scand., Vol. 21, (1967), pp. 110–121. Zbl0167.28401

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