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Discussiones Mathematicae General Algebra and Applications 23(1) (2003) 13-18
DOI: https://doi.org/10.7151/dmgaa.1060

A SCHEME FOR CONGRUENCE SEMIDISTRIBUTIVITY 

Ivan Chajda1 Department of Algebra and Geometry Palacký University of Olomouc Tomkova 40, CZ-77900 Olomouc, Czech Republic e-mail: chajda@risc.upol.cz

Eszter K. Horváth2 Bolyai Institute, University of Szeged Aradi vértanúk tere 1, H-6720 Szeged, Hungary e-mail: horeszt@math.u-szeged.hu

Abstract

A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧ -semidistributive law.

Keywords: ∧ -semidistributivity, generalized semidistribitive law, triangular scheme.

2000 Mathematics Subject Classification: 08A30, 08B10, 06D99.

References

[1]	I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo 2003.
[2]	I. Chajda and E.K. Horváth, A triangular scheme for congruence distributivity, Acta Sci. Math. (Szeged) 68 (2002), 29-35.
[3]	G. Czédli, Weak congruence semidistributivity laws and their conjugates, Acta Math. Univ. Comenian. 68 (1999), 153-170.
[4]	W. Geyer, Generalizing semidistributivity, Order 10 (1993), 77-92.
[5]	H.P. Gumm, Geometrical methods in congruence modular algebras, Mem. Amer. Math. Soc. 45 (1983), no. 286, viii+79 pp.
[6]	K.A. Kearnes and Á. Szendrei, The relationship between two commutators, Internat. J. Algebra Comput. 8 (1998), 497-53.
[7]	P. Lipparini, Characterization of varieties with a difference term, II: neutral = meet semidistributive, Canadian Math. Bull. 41 (1988), 318-327.

Received 23 September 2002
Revised 14 May 2003 

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¹The research was supported by the Czech Government MSM 153 100011.
²The research was supported by OTKA T037877.