Geodesic
Local Malcev Conditions
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 559-568

Voir la notice de l'article provenant de la source Cambridge University Press

Let p and q be polynomial symbols of a type of algebras having operations ∨, ∧, and; (interpreted as the join, meet, and product of congruence relations). If is an algebra, L(), the local variety of , is the class of all algebras such that for each finite subset G of there is a finite subset F of such that every identity of F is also an identity of G.THEOREM. There is an algorithm which, for each inequality p≤q, and pair of integers n, k≥2, determines a set Un, k of (Malcev) equations with the property: For each algebra, p≤q is true in the congruence lattice offor each ∊L() if and only if for each finite subset F ofand integer n≥2 there is a k=k(n, F) such that U n, k are identities of F.This generalizes a corresponding result for varieties due to Wille (Kongruenzklassengeometrien, Lect. Notes in Math. Springer- Verlag, Berlin-Heidelberg, New York, 1970) and at the same time provides a more direct proof. 
Pixley, Alden F. Local Malcev Conditions. Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 559-568. doi: 10.4153/CMB-1972-098-8
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[1] 1. Day, A., A characterization of modularity for congruence lattices of algebras, Canad. Math. Bull. 12(1969), 167-173. Google Scholar

[2] 2. Foster, A. L., Functional completeness in the small. Algebraic cluster theorems and identities, Math. Ann. 143(1961), 29-58. Google Scholar

[3] 3. Grätzer, G., Two Malcev type theorems in universal algebra, J. Comb. Theory. 8 (1970), 334-342. Google Scholar

[4] 4. Tah-Kai, Hu, On the fundamental subdirect factorization theorems of primal algebra theory, Math. Z. 112(1969), 154-162. Google Scholar

[5] 5. Tah-Kai, Hu and Philip, Kelenson, Independence and direct factorization of universal algebras, Math. Nachr. 51 (1971), 83-99. Google Scholar

[6] 6. Jónsson, B., Algebras whose congruence lattices are distributive, Math. Scand. 21 (1967), 110-121. Google Scholar

[7] 7. Malcev, A. I., On the general theory of algebraic systems, Mat. Sb. (77) 35 (1954), 3-20. Google Scholar

[8] 8. Pixley, A. F., Distributivity and permutability of congruences in equational classes, Proc. Amer. Math. Soc. 14 (1963), 105-109. Google Scholar

[9] 9. Pixley, A. F., 9 The ternary discriminator function in universal algebra, Math. Ann. 191 (1971), 167-180. Google Scholar

[10] 10. Wille, R., Kongruenzklassengeometrien, Lecture Notes in Math. 113, Springer-Verlag, Berlin-Heidelberg-New York, 1970. Google Scholar

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