Definable relations in finite-dimensional subspace lattices with involution

Cited 1 time in webofscience Cited 0 time in scopus
  • Hit : 276
  • Download : 0
For a large class of finite dimensional inner product spaces V, over division *- rings F, we consider definable relations on the subspace lattice L(V) of V, endowed with the operation of taking orthogonals. In particular, we establish translations between the relevant first order languages, in order to associate these relations with definable and invariant relations on F- focussing on the quantification type of defining formulas. As an intermediate structure we consider the *- ring R(V) of endomorphisms of V, thereby identifying L(V) with the lattice of right ideals of R(V), with the induced involution. As an application, model completeness of F is shown to imply that of R(V) and L(V).
Publisher
SPRINGER BASEL AG
Issue Date
2018-09
Language
English
Article Type
Article
Citation

ALGEBRA UNIVERSALIS, v.79, no.3

ISSN
0002-5240
DOI
10.1007/s00012-018-0553-5
URI
http://hdl.handle.net/10203/245902
Appears in Collection
CS-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 1 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0