Publication at Faculty of Mathematics and Physics |
2023
Abstract
In this paper, the authors consider the concept of homomorphic equivalence, where two clones A and B are so related if and only if there are clone homomorphisms from A to B and vice versa, and prove that there are 2ℵ0 many equivalence classes of clones of self-dual operations, operations preserving the relation {(0,1),(1,2),(0,2)}. Furthermore, clones of self-dual operations with respect to the binary relation <=Minor defined by a minor preserving map are described.
The authors also discuss some minor conditions on any clones A and B such that ANEITHER LESS-THAN NOR EQUAL TOB; a minor condition that holds in A but not in B is given. In the last section, some conjectures are proposed.