Circular planar nearrings: geometrical and combinatorial aspects

Details Circular planar nearrings: geometrical and combinatorial aspects Circular planar nearrings: geometrical and combinatorial aspects

2010-12-06

arxiv.org/abs/1012.1059v5

Mathematics

Rings and Algebras

12 pages

Scientific paper

Let $(N,\Phi)$ be a circular Ferrero pair. We define the disk with center $b$ and radius $a$, $\mathcal{D}(a;b)$, as \[\mathcal{D}(a;b)=\{x\in \Phi(r)+c\mid r\neq 0,\ b\in \Phi(r)+c,\ |(\Phi(r)+c)\cap (\Phi(a)+b)|=1\}.\] We prove that in the field-generated case there are many analogies with the Euclidean geometry. Moreover, if $\mathcal{B}^{\mathcal{D}}$ is the set of all disks, then, in some interesting cases, we show that the incidence structure $(N,\mathcal{B}^{\mathcal{D}},\in)$ is actually a balanced incomplete block design.

Affiliated with

Also associated with

No associations

Rating

Circular planar nearrings: geometrical and combinatorial aspects does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Circular planar nearrings: geometrical and combinatorial aspects, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Circular planar nearrings: geometrical and combinatorial aspects will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-166862