Definability of principal congruences in equivalential algebras

PaweŁ Idziak; Andrzej Wroński

Colloquium Mathematicae (1998)

  • Volume: 74, Issue: 2, page 225-238
  • ISSN: 0010-1354

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Idziak, PaweŁ, and Wroński, Andrzej. "Definability of principal congruences in equivalential algebras." Colloquium Mathematicae 74.2 (1998): 225-238. <http://eudml.org/doc/210512>.

@article{Idziak1998,
author = {Idziak, PaweŁ, Wroński, Andrzej},
journal = {Colloquium Mathematicae},
keywords = {Mal'tsev conditions; congruence permutable variety; principal congruences; equivalential algebras; Boolean groups; Brouwerian semilattices; equivalential reducts},
language = {eng},
number = {2},
pages = {225-238},
title = {Definability of principal congruences in equivalential algebras},
url = {http://eudml.org/doc/210512},
volume = {74},
year = {1998},
}

TY - JOUR
AU - Idziak, PaweŁ
AU - Wroński, Andrzej
TI - Definability of principal congruences in equivalential algebras
JO - Colloquium Mathematicae
PY - 1998
VL - 74
IS - 2
SP - 225
EP - 238
LA - eng
KW - Mal'tsev conditions; congruence permutable variety; principal congruences; equivalential algebras; Boolean groups; Brouwerian semilattices; equivalential reducts
UR - http://eudml.org/doc/210512
ER -

References

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  1. [1] K. A. Baker, Definable normal closures in locally finite varieties of groups, Houston J. Math. 7 (1981), 467-471. Zbl0494.20012
  2. [2] J. T. Baldwin and J. Berman, The number of subdirectly irreducible algebras in a variety, Algebra Universalis 5 (1975), 379-389. Zbl0348.08002
  3. [3] J. Berman, A proof of Lyndon's finite basis theorem, Discrete Math. 29 (1980), 229-233. Zbl0449.08004
  4. [4] W. Blok, P. Köhler and D. Pigozzi, On the structure of varieties with equationally definable principal congruences II, Algebra Universalis 18 (1984), 334-379. 
  5. [5] S. Burris, An example concerning definable principal congruences, ibid. 7 (1977), 403-404. Zbl0364.08005
  6. [6] S. Burris and J. Lawrence, Definable principal congruences in varieties of rings and groups, ibid. 9 (1979), 152-164. Zbl0407.08006
  7. [7] C. C. Chang and H. J. Keisler, Model Theory, North-Holland, 1973. 
  8. [8] A. Eastman and W. Nemitz, Density and closure in implicative semilattices, Algebra Universalis 5 (1975), 1-5. 
  9. [9] H. P. Gumm and A. Ursini, Ideals in universal algebras, ibid. 19 (1984), 45-54. Zbl0547.08001
  10. [10] J. Hagemmann, On regular and weakly regular congruences, preprint 75, TH Darmstadt, 1973. 
  11. [11] P. M. Idziak, Varieties with decidable finite algebras I: Linearity, Algebra Universalis 26 (1989), 234-246. Zbl0679.08002
  12. [12] J. K. Kabziński and A. Wroński, On equivalential algebras, in: Proc. 1975 Internat. Sympos. on Multiple-Valued Logic (Indiana University, Bloomington, Ind., 1975), IEEE Comput. Soc., Long Beach, Calif., 1975, 419-428. 
  13. [13] E. Kiss, Definable principal congruences in congruence distributive varieties, Algebra Universalis 21 (1985), 213-224. Zbl0554.08006
  14. [14] P. Köhler and D. Pigozzi, Varieties with equationally definable principal congruences, ibid. 11 (1980), 213-219. Zbl0448.08005
  15. [15] R. McKenzie, Paraprimal varieties: A study of finite axiomatizability and definable principal congruences, ibid. 8 (1978), 336-348. Zbl0383.08008
  16. [16] A. F. Pixley, Principal congruence formulas in arithmetical varieties, in: Lecture Notes in Math. 1149, Springer, 1985, 238-254. Zbl0572.08003
  17. [17] G. E. Simons, Varieties of rings with definable principal congruences, Proc. Amer. Math. Soc. 87 (1983), 367-402. Zbl0512.16017
  18. [18] A. Wroński, On the free equivalential algebra with three generators, Bull. Sec. Logic Polish Acad. Sci. 22 (1993), 37-39. Zbl0793.03078

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