Details
| Original language | German |
|---|---|
| Pages (from-to) | 69-89 |
| Number of pages | 21 |
| Journal | Journal of Geometry |
| Volume | 1 |
| Issue number | 1 |
| Publication status | Published - Mar 1971 |
Abstract
Let σ > 0 be an integer. A projective σ-fibre space is formed by a covering of a projective geometry with σ-1 isomorphic geometries. The double elliptic space (Sphärischer Raum) is an example of a 2-fibre space. This note deals with projective σ-fibre spaces which are structured by multy valued orderfunctions (This notion was introduced by W. JUNKERS [2] for projective geometries) the range of which is a group G. If such an ordered σ-fibre space has the property |G|=σ, it is called projective G-fibre space. It is proved that the desarguesian projective G-fibre spaces V are exactly those, which are induced by a vector space S over a field K (commutative or not) having a normal subgroup P {normal subgroup of} K*(·) with K*′ ⊂P such that G≅K*/P and S≅V*/P. This theorem is a generalization of the well-known case P=K*.
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Geometry, Vol. 1, No. 1, 03.1971, p. 69-89.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Projektive G-Faserräume
AU - Hotje, Herbert
PY - 1971/3
Y1 - 1971/3
N2 - Let σ > 0 be an integer. A projective σ-fibre space is formed by a covering of a projective geometry with σ-1 isomorphic geometries. The double elliptic space (Sphärischer Raum) is an example of a 2-fibre space. This note deals with projective σ-fibre spaces which are structured by multy valued orderfunctions (This notion was introduced by W. JUNKERS [2] for projective geometries) the range of which is a group G. If such an ordered σ-fibre space has the property |G|=σ, it is called projective G-fibre space. It is proved that the desarguesian projective G-fibre spaces V are exactly those, which are induced by a vector space S over a field K (commutative or not) having a normal subgroup P {normal subgroup of} K*(·) with K*′ ⊂P such that G≅K*/P and S≅V*/P. This theorem is a generalization of the well-known case P=K*.
AB - Let σ > 0 be an integer. A projective σ-fibre space is formed by a covering of a projective geometry with σ-1 isomorphic geometries. The double elliptic space (Sphärischer Raum) is an example of a 2-fibre space. This note deals with projective σ-fibre spaces which are structured by multy valued orderfunctions (This notion was introduced by W. JUNKERS [2] for projective geometries) the range of which is a group G. If such an ordered σ-fibre space has the property |G|=σ, it is called projective G-fibre space. It is proved that the desarguesian projective G-fibre spaces V are exactly those, which are induced by a vector space S over a field K (commutative or not) having a normal subgroup P {normal subgroup of} K*(·) with K*′ ⊂P such that G≅K*/P and S≅V*/P. This theorem is a generalization of the well-known case P=K*.
UR - http://www.scopus.com/inward/record.url?scp=34250463276&partnerID=8YFLogxK
U2 - 10.1007/BF02150276
DO - 10.1007/BF02150276
M3 - Artikel
AN - SCOPUS:34250463276
VL - 1
SP - 69
EP - 89
JO - Journal of Geometry
JF - Journal of Geometry
SN - 0047-2468
IS - 1
ER -