On projective embeddings of partial planes and rank-three matroids

被引：3

作者：

Kalhoff, F ^{[1
]}

机构：

[1] UNIV PASSAU,FAK MATH & INFORMAT,D-94030 PASSAU,GERMANY

来源：

DISCRETE MATHEMATICS | 1997年 / 163卷 / 1-3期

关键词：

rank; 3; matroids; linear spaces; partial planes; projective embeddings; finite projective planes; translation planes; Lenz-Barlotti classification; (non-associative) division algebras;

D O I：

10.1016/0012-365X(95)00310-S

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Any finite partial plane f, and thus any finite linear space and any (simple) rank-three matroid, can be embedded into a translation plane. It even turns out, that f is embeddable into a projective plane of Lenz class V, and that the characteristic of this plane can be chosen arbitrarily. In particular, any rank three matroid is realizable over a (not necessarily associative) division algebra.

引用

页码：67 / 79

页数：13

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