Minkowski difference and Sallee elements in an ordered semigroup

Danuta Borowska, and Jerzy Grzybowski. "Minkowski difference and Sallee elements in an ordered semigroup." Commentationes Mathematicae 47.1 (2007): null. <http://eudml.org/doc/291974>.

@article{DanutaBorowska2007,
abstract = {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.},
author = {Danuta Borowska, Jerzy Grzybowski},
journal = {Commentationes Mathematicae},
keywords = {Minkowski difference; Sallee elements; semigroups},
language = {eng},
number = {1},
pages = {null},
title = {Minkowski difference and Sallee elements in an ordered semigroup},
url = {http://eudml.org/doc/291974},
volume = {47},
year = {2007},
}

TY - JOUR
AU - Danuta Borowska
AU - Jerzy Grzybowski
TI - Minkowski difference and Sallee elements in an ordered semigroup
JO - Commentationes Mathematicae
PY - 2007
VL - 47
IS - 1
SP - null
AB - 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.
LA - eng
KW - Minkowski difference; Sallee elements; semigroups
UR - http://eudml.org/doc/291974
ER -