Minimal underlying division rings of sets of points of a projective space |
| |
Authors: | Bart De Bruyn Antonio Pasini |
| |
Institution: | aDepartment of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281 (S22), B-9000 Gent, Belgium;bDipartimento di Scienze Matematiche e Informatiche, Università di Siena, Pian dei Mantellini, 44, I-53100 Siena, Italy |
| |
Abstract: | Let V be a vector space over a division ring K. Let P be a spanning set of points in Σ:=PG(V). Denote by K(P) the family of sub-division rings F of K having the property that there exists a basis BF of V such that all points of P are represented as F-linear combinations of BF. We prove that when K is commutative, then K(P) admits a least element. When K is not commutative, then, in general, K(P) does not admit a minimal element. However we prove that under certain very mild conditions on P, any two minimal elements of K(P) are conjugate in K, and if K is a quaternion division algebra then K(P) admits a minimal element. |
| |
Keywords: | Division rings Projective embeddings |
本文献已被 ScienceDirect 等数据库收录! |
|