Affine geometry of modules over a ring with invariant basis number

DOI10.1134/S000143460711020XzbMath1147.51001OpenAlexW3161033674MaRDI QIDQ941911

T. G. Kvirikashvili, A. A. Lashkhi

Publication date: 2 September 2008

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s000143460711020x

zbMATH Keywords

complete latticeprojective geometrycollineationaffine ring geometryfundamental theorem of affine geometrymodules over IBN-rings

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Ring geometry (Hjelmslev, Barbilian, etc.) (51C05)

Related Items (7)

Fundamental theorem of affine geometry for Lie algebras ⋮ Free products in the category of \(A\)-groups over a ring \(A\). ⋮ Geometrical maps in ring affine geometries ⋮ Power groups. ⋮ Divisible designs, Laguerre geometry, and beyond ⋮ Chain conditions in \(D\)-semimodular lattices. ⋮ Algebraic representation of mappings between submodule lattices.

Cites Work

• About full or injective lineations
• Fundamentalsatz für affine Räume über Moduln
• On the Fundamental Theorem of Affine Geometry
• Definition of Affine Geometry by a Group of Transformations
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