NDLI: Closure planes

Content Provider	Springer Nature Link
Author	Matthews, Rex W. Coulter, Robert S.
Copyright Year	2015
Abstract	We introduce a simple algebraic method for constructing infinite affine (and projective) planes from an infinite set of finite planes of prime power order stemming from a “root” plane. The construction uses finite fields and infinite extensions of finite fields in a critical way. We obtain a classical-looking result which states that if the construction succeeds over the algebraic closure of a finite field, then both the infinite plane and the original root plane must be Desarguesian. The Lenz–Barlotti types for these planes are then linked to the Lenz–Barlotti type of the root plane. Examples are then given. These show that under suitable conditions, the method can yield infinitely many non-isomorphic infinite planes. These examples are of Lenz–Barlotti types II.1 and V.1.
Ending Page	749
Page Count	15
Starting Page	735
File Format	PDF
ISSN	09259899
e-ISSN	15729192
Journal	Journal of Algebraic Combinatorics
Issue Number	3
Volume Number	43
Language	English
Publisher	Springer US
Publisher Date	2015-12-21
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Affine and projective planes Polynomials (irreducibility, etc.) Lenz–Barlotti classification Closures of fields Convex and Discrete Geometry Computer Science Planar ternary rings Finite geometries Order, Lattices, Ordered Algebraic Structures Group Theory and Generalizations Infinite affine planes Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Planar functions and planes of Lenz-Barlotti class (1997)

A family of semifields in characteristic 2

A Non-Existence Result For Finite Projective Planes In Lenz-Barlotti Class I.4

An algebraic approach to finite projective planes

Low-degree planar monomials in characteristic two

Symplectic spreads, planar functions, and mutually unbiased bases

Some Projective Planes of Lenz-Barlotti Class I

Basic coset geometries

Planar Groups

Closure planes

Similar Documents

Planar functions and planes of Lenz-Barlotti class (1997)

A family of semifields in characteristic 2

A Non-Existence Result For Finite Projective Planes In Lenz-Barlotti Class I.4

An algebraic approach to finite projective planes

Low-degree planar monomials in characteristic two

Symplectic spreads, planar functions, and mutually unbiased bases

Some Projective Planes of Lenz-Barlotti Class I

Basic coset geometries

Planar Groups

Closure planes