2020/05/30 by Stefano Fioravanti, Fioravanti, Stefano
Computer Science · Mathematics · #08A40 #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2006.00291
openalex publication_date 2020/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate finitary functions from ℤpq to ℤpq for two distinct prime numbers p and q. We show that the lattice of all clones on the set ℤpq which contain the addition of ℤpq is finite. We provide an upper bound for the cardinality of this lattice through an injective function to the direct product of the lattice of all (ℤp,ℤq)-linearly closed clonoids to the p+1 power and the lattice of all (ℤq,ℤp)-linearly closed clonoids to the q+1 power. These lattices are studied in arXiv:1910.11759 and there we can find the exact cardinality of them. Furthermore, we prove that these clones can be generated by a set of functions of arity at most max(\p,q\).