HYPERCLONE LATTICE AND EMBEDDINGS
Jovanka Pantović, Biljana Rodic, Gradimir Vojvodić · 2006
Abstract. In this paper, hyperclone lattice is studied via three kinds of embeddings. One is from the clone lattice on A to the hyperclone lattice on A, the second is from the hyperclone lattice on A to the clone lattice on P (A) \\ {∅} and the third one is from the hyperclone lattice on A ′ to the hyperclone lattice on A, for A ′ ⊂ A and the finite set A. The second map has usually been used for the description of hyperclone lattice, but one can see from this paper that hyperclone lattice on A is in some way thin in the clone lattice on P (A) \\ {∅}. However, we show that the first and the third embeddings are full order embeddings and they are used to lift several properties.