Journal article
Inducing lattice maps by semilinear isomorphisms
The Rocky Mountain journal of mathematics, Vol.14(2), pp.475-486
1984
DOI: 10.1216/RMJ-1984-14-2-475
Abstract
In this paper all modules are left modules and all module homomorphisms act on the right. Ring homomorphisms are written on the left. If M is a module, let L(M) denote the lattice of submodules of M. The Fundamental Theorem of Projective Geometry asserts that if D and AT are two division rings and X: L(D) -> L(K) is a lattice isomorphism between two three-dimensional free modules, then X is induced by a semilinear isomorphism. This means that there is an additive isomorphism L: D -> KTM and a ring isomorphism a:D K such that (X)L = X(X) for each X e L(DTM) and (dV)L = a(d)(V)L for all V e DTM and deD. For convenience the phrase "lattice isomorphism X: A -> 5 " will be used to mean X: L(A) -> L(B) is a lattice isomorphism. There has been some interest in generalizing this theorem to larger classes of rings. We prove here:
Details
- Title: Subtitle
- Inducing lattice maps by semilinear isomorphisms
- Creators
- V. P Camillo
- Resource Type
- Journal article
- Publication Details
- The Rocky Mountain journal of mathematics, Vol.14(2), pp.475-486
- DOI
- 10.1216/RMJ-1984-14-2-475
- ISSN
- 0035-7596
- eISSN
- 1945-3795
- Language
- English
- Date published
- 1984
- Academic Unit
- Mathematics
- Record Identifier
- 9983985872802771
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