8 citations · 24 across the 20 of their papers we have counts for
21 papers
Congruence Preservation, Lattices and Recognizability
Patrick Cegielski, Serge Grigorieff, Irene Guessarian
We study in general algebras Gratzer's notion of congruence preserving function, characterizing functions in terms of stability under inverse image of particular Boolean algebras o…
Randomness and uniform distribution modulo one
Verónica Becher, Serge Grigorieff
We elaborate the notions of Martin-Löf and Schnorr randomness for real numbers in terms of uniform distribution of sequences. We give a necessary condition for a real number to be…
The algebra of binary trees is affine complete
Andre Arnold, Patrick Cegielski, Serge Grigorieff +1
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of binar…
The algebra of complete binary trees is affine complete
A. Arnold, P. Cegielski, S. Grigorieff +1
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of compl…
Congruence Preservation, Lattices and Recognizability
Patrick Cegielski, Serge Grigorieff, Irene Guessarian
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalenc…
Congruence Preserving Functions on Free Monoids
Patrick Cégielski, Serge Grigorieff, Irène Guessarian
A function on an algebra is congruence preserving if, for any congruence, it maps congruent elements to congruent elements. We show that, on a free monoid generated by at least 3 l…