Geodesic
Minkowski difference and Sallee elements in an ordered semigroup
Commentationes Mathematicae, Tome 47 (2007) no. 1, pp. 77-83.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In the manner of Pallaschke and Urbański ([5], chapter 3) we generalize the notions of the Minkowski difference and Sallee sets to a semigroup. Sallee set (see [7], definition of the family \(S\) on p. 2) is a compact convex subset \(A\) of a topological vector space \(X\) such that for all subsets \(B\) the Minkowski difference \(A -B\) of the sets \(A\) and \(B\) is a summand of \(A\). The family of Sallee sets characterizes the Minkowski subtraction, which is important to the arithmetic of compact convex sets (see [5]). Sallee polytopes are related to monotypic polytopes (see [4]). We generalize properties of Minkowski difference and Sallee sets to semigroup and investigate the families of Sallee elements in several specific semigroups.
DOI : 10.14708/cm.v47i1.5239
Mots-clés : Minkowski difference, Sallee elements, semigroups 
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Danuta Borowska; Jerzy Grzybowski. Minkowski difference and Sallee elements in an ordered semigroup. Commentationes Mathematicae, Tome 47 (2007) no. 1, pp.  77-83. doi : 10.14708/cm.v47i1.5239. http://geodesic.mathdoc.fr/articles/10.14708/cm.v47i1.5239/

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