Definability of principal congruences in equivalential algebras

• Autorzy: PaweŁ M. Idziak , Andrzej Wroński
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1997
• Tom: 74
• Numer: 2
• Strony: 225-238

Daty

wydano

1998

otrzymano

1996-05-28

poprawiono

1997-01-13

Twórcy

autor

PaweŁ M. Idziak

• Computer Science Department, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland

autor

Andrzej Wroński

• Department of Logic, Jagiellonian University, Grodzka 52, 31-044 Kraków, Poland

Bibliografia

• [1] K. A. Baker, Definable normal closures in locally finite varieties of groups, Houston J. Math. 7 (1981), 467-471.
• [2] J. T. Baldwin and J. Berman, The number of subdirectly irreducible algebras in a variety, Algebra Universalis 5 (1975), 379-389.
• [3] J. Berman, A proof of Lyndon's finite basis theorem, Discrete Math. 29 (1980), 229-233.
• [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] S. Burris, An example concerning definable principal congruences, ibid. 7 (1977), 403-404.
• [6] S. Burris and J. Lawrence, Definable principal congruences in varieties of rings and groups, ibid. 9 (1979), 152-164.
• [7] C. C. Chang and H. J. Keisler, Model Theory, North-Holland, 1973.
• [8] A. Eastman and W. Nemitz, Density and closure in implicative semilattices, Algebra Universalis 5 (1975), 1-5.
• [9] H. P. Gumm and A. Ursini, Ideals in universal algebras, ibid. 19 (1984), 45-54.
• [10] J. Hagemmann, On regular and weakly regular congruences, preprint 75, TH Darmstadt, 1973.
• [11] P. M. Idziak, Varieties with decidable finite algebras I: Linearity, Algebra Universalis 26 (1989), 234-246.
• [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] E. Kiss, Definable principal congruences in congruence distributive varieties, Algebra Universalis 21 (1985), 213-224.
• [14] P. Köhler and D. Pigozzi, Varieties with equationally definable principal congruences, ibid. 11 (1980), 213-219.
• [15] R. McKenzie, Paraprimal varieties: A study of finite axiomatizability and definable principal congruences, ibid. 8 (1978), 336-348.
• [16] A. F. Pixley, Principal congruence formulas in arithmetical varieties, in: Lecture Notes in Math. 1149, Springer, 1985, 238-254.
• [17] G. E. Simons, Varieties of rings with definable principal congruences, Proc. Amer. Math. Soc. 87 (1983), 367-402.
• [18] A. Wroński, On the free equivalential algebra with three generators, Bull. Sec. Logic Polish Acad. Sci. 22 (1993), 37-39.