Ivana Varga – Clones of compatible operations on ring ${\mathbb{Z}}_8$

Pavol Jozef Safarik University in Košice, Faculty of Science
The study of clones of specific operations on an algebra has become an interesting and nontrivial topic in universal algebra. We investigate the interval $I(8)$ in the lattice of clones on the ring ${\mathbb{Z}}_8$ between the clone of polynomial operations and the clone of congruence preserving operations. All clones in this interval are known and described by means of generators. In this talk, We characterize each of these clones by the property of preserving a small set of relations.