# Minkowski difference and Sallee elements in an ordered semigroup

Danuta Borowska; Jerzy Grzybowski

Commentationes Mathematicae (2007)

- Volume: 47, Issue: 1
- ISSN: 2080-1211

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topDanuta 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 -

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