Title data
Kiermaier, Michael ; Landjev, Ivan:
Designs in projective Hjelmslev spaces.
In:
Lavrauw, Michel (Hrsg.): Theory and Applications of Finite Fields. -
Providence, RI
: American Mathematical Society
,
2012
. - pp. 111-121
. - (Contemporary Mathematics
; 579
)
ISBN 978-0-8218-5298-9
DOI: https://doi.org/10.1090/conm/579/11524
Project information
Project title: |
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Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract in another language
In this paper, we define analogs of designs in the Grassmanian of all submodules of given shape in the free module Rⁿ, where R is a finite chain ring. We consider τ-designs for τ=(m,0,...,0). Such designs are equivalent to spreads in projective Hjelmslev geometries. We give examples of line spreads in which no two lines are neighbours in the 3-dimensional Hjelmslev geometries over the chain rings with four and nine elements. We prove that non-trivial line spreads exist in all 3-dimensional projective Hjelmslev geometries over a commutative chain ring R. We give a necessary and sufficient condition for the existence of spreads of Hjelmslev subspaces. We prove that in case of spreads of non-free subspaces, this necessary condition is not sufficient.
Further data
Item Type: | Article in a book |
---|---|
Refereed: | Yes |
Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |
Result of work at the UBT: | Yes |
DDC Subjects: | 500 Science > 510 Mathematics |
Date Deposited: | 20 Nov 2014 08:04 |
Last Modified: | 20 Nov 2014 08:04 |
URI: | https://eref.uni-bayreuth.de/id/eprint/3728 |