×

zbMATH — the first resource for mathematics

On the approximation of the Boolean powers by Cartesian powers. (English) Zbl 0844.08002
Summary: On the basis of the Mal’tsev-Cleave theorem on quasi-universal formulas, it is proved that a number of properties of congruences, tolerances, quasiorders can be transported from finite Cartesian powers of algebraic systems to any Boolean powers.
MSC:
08A05 Structure theory of algebraic structures
08A30 Subalgebras, congruence relations
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] Foster A. L.: Functional completeness in the small. Algebraic structure theorems and identities. Math. Ann., v. 143, N 1, 1961, 29-53. · Zbl 0095.02201
[2] Burris S.: Boolean powers. Alg. Univ., v. 5, N 3, 1975, 341-360. · Zbl 0328.08003
[3] Pinus A. G.: Boolean constructions in universal algebra. Kluwer Academ. Publish., Dordrecht-Boston-London, 1993. · Zbl 0792.08001
[4] Pinus A. G.: On the covers in epimorphism skeletons of varreties of algebras. Algebra and logic, v. 27, N 3, 1988, 316-326) · Zbl 0666.08004
[5] Malcev A. I.: The model correspondences. Izvestia AN SSSR, ser. math., v. 23, N 3, 1959, 313-336)
[6] Cleave I. P.: Local properties of systems. J. London Math. Soc. (1), v. 44, N 1, 1969, 121-130, Addendum., J. London. Math. Soc. (2), v. 1, N 2, 1969, p. 384. · Zbl 0169.00701
[7] Kargapolov M. I., Merzljakov, Ju. I.: Fundaments of the theory of groups. Nauka, Moscow, 1972) · Zbl 0549.20001
[8] Chajda I.: Algebraic theory of tolerance relations. UP Olomouc, Monography series., 1991. · Zbl 0747.08001
[9] Pinus A. G., Chajda I.: Quasiorders on the universal algebras. Algebra and logic, v. 32, N 3, 1993) · Zbl 0824.08002
[10] Fraser G. A., Horn A.: Congruence relations in direct products. Proc. Amer. Math. Soc., v. 26, N 2, 1970, 390-394. · Zbl 0241.08004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.