Geodesic
Extending Algebras to Model Congruence Schemes
Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 257-276

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

This paper is concerned with the description of principal congruence relations. Given elements a and b of a universal algebra , let θ(a, b) denote the smallest congruence relation on containing the pair 〈a, b〉. One of the earliest characterizations of θ(a, b) is Mal'cev's well-known result [5, Theorem 1.10.3], which says that c ≡ d(θ(a, b)) if and only if there exists a sequence z 0, z 1, ..., zn of elements of and a sequence f 1, f 2, ..., fn of unary algebraic functions such that c = z 0, d = zn , and for each i = 1, ..., n, Although this describes θ(a, b) in terms of a set of unary algebraic functions, it is not possible to predict the number or complexity of the unary functions used independently of the choice of a, b, c and d. Several recent papers ([1], [2], [3], [4], [6]) investigate classes of algebras in which principal congruences are simpler. 
Berman, J.; Grätzer, G.; Platt, C. R. Extending Algebras to Model Congruence Schemes. Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 257-276. doi: 10.4153/CJM-1986-012-8
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