Projective mappings between projective lattice geometries

Pfeiffer, Thorsten; Schmidt, Stefan E.

doi:10.1007/bf01222858

Cited by 2 publications

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“…It generalized a former version due to Brauner [1] on linear maps. In the case of projective lattice geometries, these linear maps are discussed in [14]. Recently, a further generalization of the fundamental theorem for classical projective spaces appeared in [7].…”

Section: Introductionmentioning

confidence: 99%

Morphisms of projective spaces over rings

Faure¹

2004

Advg

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The fundamental theorem of projective geometry is generalized for projective spaces over rings. Let R M and S N be modules. Provided some weak conditions are satisfied, a morphism g : PðMÞnE ! PðNÞ between the associated projective spaces can be induced by a semilinear map f : M ! N. These conditions are satisfied for instance if S is a left Ore domain and if the image of g contains three independent free points. No assumptions are made on the module M, and both modules may have some torsion.

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Section: Introductionmentioning

confidence: 99%

Morphisms of projective spaces over rings

Faure¹

2004

Advg

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“…A significant generalization of linear mappings to projective and affine lattice geometries has been given by Pfeiffer [45], [46], and Pfeiffer and Schmidt [47]. See furthermore Faigle [20].…”

Section: Lattice Geometriesmentioning

confidence: 99%

Weak Linear Mappings -- A Survey

Havlicek

2012

Preprint

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There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some detail and report on generalizations to other spaces.We shall come across partially defined mappings. The notation ϕ : P ≻→ P ′ is used in order to point out that ϕ is a mapping with domain dom ϕ ⊂ P and image set im ϕ ⊂ P ′ . The exceptional set of ϕ (with respect to P) is given as ex ϕ := P \ dom ϕ. The mapping ϕ is said to be globally defined (with respect to P) provided that ex ϕ is empty. The notation ϕ : P → P ′ is maintained for globally defined mappings only.If we are given any subset M ⊂ P, then {X ϕ | X ∈ M ∩ dom ϕ} is a well-defined set. By abuse of notation, it is written as M ϕ . Hence M ϕ = ∅ exactly for M ⊂ ex ϕ.

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Projective mappings between projective lattice geometries

Cited by 2 publications

References 5 publications

Morphisms of projective spaces over rings

Morphisms of projective spaces over rings

Weak Linear Mappings -- A Survey

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