2020/09/16 by Fioravanti, Stefano
#08A40 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2009.08256
We investigate finitary functions from ℤn to ℤn for a squarefree number n. We show that the lattice of all clones on the squarefree set ℤp1⋯ pm which contain the addition of ℤp1⋯ pm is finite. We provide an upper bound for the cardinality of this lattice through an injective function to the direct product of the lattices of all (ℤpi, \mathbbFi)-linearly closed clonoids, L(ℤpi, \mathbbFi), to the pi+1 power, where \mathbbFi = ∏_j ∈ \1,…,m\\backslash \i\ℤpj. These lattices are studied in the litterature and we can find an upper bound for cardinality of them. Furthermore, we prove that these clones can be generated by a set of functions of arity at most max(p1,…,pm).