Details
| Originalsprache | Deutsch |
|---|---|
| Seiten (von - bis) | 69-89 |
| Seitenumfang | 21 |
| Fachzeitschrift | Journal of Geometry |
| Jahrgang | 1 |
| Ausgabenummer | 1 |
| Publikationsstatus | Veröffentlicht - März 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 Sachgebiete
- Mathematik (insg.)
- Geometrie und Topologie
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in: Journal of Geometry, Jahrgang 1, Nr. 1, 03.1971, S. 69-89.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -