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Features of Interaction Between Formal Concept Analysis and Algebraic Geometry

  • Tim Becker
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3626)

Abstract

This paper contributes to Algebraic Concept Analysis by examining connections between Formal Concept Analysis and Algebraic Geometry. The investigations are based on polynomial contexts (over a field K in n variables) which are defined by \({\mathbb{K}}^{(n)} := (K^n,K[x_1,\ldots,x_n],\perp)\) where \(a \perp f :\Leftrightarrow f(a)=0\) for aK n and any polynomial fK[x 1,...,x n ]. Important notions of Algebraic Geometry such as algebraic varieties, coordinate algebras, and polynomial morphisms are connected to notions of Formal Concept Analysis. That allows to prove many interrelating results between Algebraic Geometry and Formal Concept Analysis, even for more abstract notions such as affine and projective schemes.

Keywords

Topological Space Algebraic Geometry Prime Ideal Irreducible Component Maximal Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Tim Becker
    • 1
  1. 1.Institute for Medical Biometry, Informatics and EpidemiologyBonn

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