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Rich countable epimorphism skeletons of discriminator varieties. (English. Russian original) Zbl 0712.08008

Sib. Math. J. 31, No. 3, 465-472 (1990); translation from Sib. Mat. Zh. 31, No. 3(181), 125-134 (1990).
More or less completing his results from previous papers, the author shows that a discriminator variety \({\mathfrak M}\) which is not finitely generated but either has finite signature or has singleton subalgebras of all its algebras is universal for countable quasiordered sets S, i.e. S can be represented by countable \({\mathfrak M}\)-algebras and the quasiorder “epic quotient”.
Reviewer: J.R.Isbell

MSC:

08B99 Varieties
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[1] A. G. Pinus, ?On the relations of epimorphism and embeddability on congruence-distributive varieties,? Algebra Logika,24, NO. 5, 588-607 (1985).
[2] A. G. Pinus, Congruence-Modular Varieties of Algebras [in Russian], Irkutsk State Univ. (1986). · Zbl 0714.08003
[3] A. G. Pinus, ?On simple epimorphism skeletons of congruence-distributive varieties,? Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 67-70 (1987). · Zbl 0652.08003
[4] A. G. Pinus, ?On coverings in epimorphism skeletons of varieties of algebras,? Algebra Logika,27, No. 3, 316-326 (1988).
[5] A. G. Pinus, ?Congruence-distributive varieties of algebras,? Progress in Science. Algebra, Geometry, and Toplogy [in Russian], Vol. 26, Bsesoyuz. Inst. Nauch. i Tekh. Informatsii, Moscow (1988), pp. 45-83. · Zbl 0679.08004
[6] A. G. Pinus, ?On the number of incomparables in countable epimorphism skeletons of discriminator varieties,? Algebra Logika,28, No. 3, 311-323 (1989).
[7] G. Grätzer, Universal Algebra, 2nd Ed., Springer-Verlag, Berlin-Heidelberg (1979).
[8] S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York-Heidelberg-Berlin (1981). · Zbl 0478.08001
[9] H. Werner, Discriminator Algebras, Akademie Verlag, Berlin (1978).
[10] G. A. Fraser and A. Horn, ?Congruence relations in direct product,? Proc. Am. Math. Soc.,26, No. 3, 390-394 (1970). · Zbl 0241.08004 · doi:10.1090/S0002-9939-1970-0265258-1
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