Projects per year
Abstract
A map f from a vector space V into its underlying field F is called semi-homogeneous if f(kv)=kf(v) holds for all k in Im(f) and v in V. This means that we have f(f(w)v)=f(w)f(v) for all v,w in V. If we define the operation * on V via w*v:=f(w)v, this equation makes (V,+,*) into a planar nearring. So we have an (almost) 1-1-correspondence between semi-homogeneous maps and planar nearrings on a vector space V. This enables a complete characterization of semi-homogeneous maps. One can even generalize this to the much more general case of actions of groups on sets.
| Original language | English |
|---|---|
| Title of host publication | A Panorama of Mathematics: Pure and Applied |
| Place of Publication | Providence, RI, USA |
| Publisher | American Mathematical Society |
| Pages | 187-196 |
| Number of pages | 9 |
| Volume | 658 |
| ISBN (Print) | 978-1-4704-2902-7 |
| DOIs | |
| Publication status | Published - 2016 |
Publication series
| Name | Contemporary Mathematics |
|---|---|
| ISSN (Print) | 0271-4132 |
Fields of science
- 101 Mathematics
- 101001 Algebra
- 101005 Computer algebra
- 101013 Mathematical logic
- 102031 Theoretical computer science
JKU Focus areas
- Computation in Informatics and Mathematics
- Engineering and Natural Sciences (in general)
Projects
- 1 Finished
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Nearrings with a right identity
Wendt, G. (PI)
15.07.2011 → 14.07.2014
Project: Funded research › FWF - Austrian Science Fund