Uniformity of congruences in coherent varieties

Ivan Chajda

Mathematica Bohemica (2000)

  • Volume: 125, Issue: 3, page 269-273
  • ISSN: 0862-7959

Abstract

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An algebra a is uniform if for each θ ∈ a , every two classes of θ have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.

How to cite

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Chajda, Ivan. "Uniformity of congruences in coherent varieties." Mathematica Bohemica 125.3 (2000): 269-273. <http://eudml.org/doc/248687>.

@article{Chajda2000,
abstract = {An algebra $a$ is uniform if for each $\theta \in a$, every two classes of $\theta $ have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.},
author = {Chajda, Ivan},
journal = {Mathematica Bohemica},
keywords = {uniformity; regularity; permutability; coherence; transferable congruences; Mal'cev condition; uniformity; regularity; permutability; coherence; transferable congruences; Mal'tsev condition},
language = {eng},
number = {3},
pages = {269-273},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Uniformity of congruences in coherent varieties},
url = {http://eudml.org/doc/248687},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Chajda, Ivan
TI - Uniformity of congruences in coherent varieties
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 3
SP - 269
EP - 273
AB - An algebra $a$ is uniform if for each $\theta \in a$, every two classes of $\theta $ have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.
LA - eng
KW - uniformity; regularity; permutability; coherence; transferable congruences; Mal'cev condition; uniformity; regularity; permutability; coherence; transferable congruences; Mal'tsev condition
UR - http://eudml.org/doc/248687
ER -

References

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  2. Chаjdа I., 10.1007/BF01194526, Algebra Universalis 17 (1983), 170-173. (1983) MR0726270DOI10.1007/BF01194526
  3. Chаjdа I., Examples of local uniformity of congruences, Acta Sci. Math. (Szeged) 52 (1988), 81-84. (1988) MR0957790
  4. Chаjdа I, Weak coherence of congruences, Czechoslovak Math. J. 41 (1991), 149-154. (1991) MR1087635
  5. Geiger D., Coherent algebras, Notices Amer. Math. Soc. 21 (1974), 74T-A130. (1974) 
  6. Krаuss P. H., Clаrk D. M., Global subdirect products, Mem. Amer. Math. Soc. 210 (1979). (1979) MR0512475
  7. McKenzie R., 10.1007/BF02483709, Algebra Universalis 15 (1982), 67-85. (1982) Zbl0505.08004MR0663953DOI10.1007/BF02483709
  8. Tаylor W., 10.1007/BF02485747, Algebra Universalis 4 (1974), 342-360. (1974) MR0376483DOI10.1007/BF02485747
  9. Thurston H. A., Derived operations and congruences, Proc. London Math. Soc. 8 (1958), 127-134. (1958) Zbl0078.01901MR0091924
  10. Werner H., 10.1007/BF02945126, Algebra Universalis 3 (1973), 263. (1973) MR0330009DOI10.1007/BF02945126

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