SKEW NEARLATTICES: SOME STRUCTURE AND
Representation Theorems · 2010
A nearlattice is a meet semilattice in which every principial order ideal is a lattice. Roughly, a skew nearlattice is a nearlattice with non-commutative meet operation; in particular, a skew nearlattice is said to be right normal (an rns-nearlattice, in short) if a weakened commutative law xyz = yxz holds. (Thus, rns-nearlattices are just right normal bands having the upper bound property.) We characterise the structure of rns- nearlattices and prove certain representation theorems for such algebras. In particular, every distributive rns-nearlattice is shown to be isomorphic to an algebra of partial functions of the kind (A,(, \) with the operation defined as follows: (' )(i) = v i i2 dom' dom and (i) = v.