Projective Klingenberg Planes Constructed with Dual Local Rings

Dayıoglu, Abdurrahman; Çelik, Basri

doi:10.1063/1.3636727

AIP Conference Proceedings

2011

DOI: 10.1063/1.3636727

|View full text |Cite

Projective Klingenberg Planes Constructed with Dual Local Rings

Abdurrahman Dayıoglu¹,

Basri Çelik²

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2013

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

The collineations which act as addition and multiplication on points in a certain class of projective Klingenberg planes

Çelik

Dayıoglu

2013

J Inequal Appl

View full text Add to dashboard Cite

Let PK 2 (Q(ε)) be the projective Klingenberg plane coordinated by the dual quaternion ring Q(ε) = Q + Qε = {x + yε | x, y ∈ Q} where Q is any quaternion ring. In this paper, we determine the addition and multiplication of the points on the line [0, 1, 0] of PK 2 (Q(ε)) as the image of some collineations of the plane PK 2 (Q(ε)). To do this, we give the collineations S a and L a . Later we show that the addition and multiplication of the nonneighbor points on the line [0, 1, 0] can be obtained as the images under that S a and L a . MSC: 51C05; 51J10; 12E15

show abstract

The collineations which act as addition and multiplication on points in a certain class of projective Klingenberg planes

Çelik

Dayıoglu

2013

J Inequal Appl

View full text Add to dashboard Cite

show abstract

On addition and multiplication of points in a certain class of projective Klingenberg planes

Çelik

Erdoğan

2013

J Inequal Appl

View full text Add to dashboard Cite

Let (O, E, U, V) be the coordination quadruple of the projective Klingenberg plane (PK-plane) coordinated with dual quaternion ring Q(ε)where Q is any quaternion ring over a field. In this paper, we define addition and multiplication of points on the line OU = [0, 1, 0] geometrically, also we give the algebraic correspondences of them. Finally, we carry over some well-known properties of ordinary addition and multiplication to our definition. MSC: 51C05; 51N35; 14A22; 16L30

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Projective Klingenberg Planes Constructed with Dual Local Rings

Cited by 2 publications

References 0 publications

The collineations which act as addition and multiplication on points in a certain class of projective Klingenberg planes

The collineations which act as addition and multiplication on points in a certain class of projective Klingenberg planes

On addition and multiplication of points in a certain class of projective Klingenberg planes

Contact Info

Product

Resources

About