SUBTRACTION-LIKE OPERATIONS IN NEARSEMILATTICES
Jānis Cı̄rulis · Demonstratio Mathematica · 2010
A nearsemilattice is a poset having the upper-bound property.A binary operation -on a poset with the least element 0 is said to be subtraction-like if x < y if and only if x -y = 0 for all x,y.Associated with such an operation is a family of partial operations l p defined by l p (x) := p -x on every initial segment [0,p]; these operations are thought of as local (sectional) complementations of some kind.We study several types of subtraction-like operations, show that each of these operations can be restored in a uniform way from the corresponding local complementations, and state some connections between properties of a (sufficiently strong) subtraction on a nearsemilattice and distributivity of the latter.