2006-12-05 Seminar

mgr Danuta Borowska, dr Jerzy Grzybowski
Subtraction and Sallee's elements in semigroups

We can define the Minkowski sum and the Minkowski subtraction in the cone of convex and compact sets. Properties of the the Minkowski subtraction were studied by G.T. Sallee, who formulated the definition of a family of sets, such that the intersection of any collection of translations of the given set is the summand of this set. The Minkowski subtraction was generalized to semigroups by H. Przybycień. During the lecture we will present some properties of the subtraction and we will give the generalization of the notion of a Sallee's set for the semigroups' elements. Moreover, interesting examples of semigroups will be presented.