Algebraic geometry over algebraic structures X: Ordinal dimension

Evelina Yur Evna Daniyarova, Alexei Georgievich Myasnikov, Vladimir Nikanorovich Remeslennikov

Research output: Contribution to journalArticlepeer-review

Abstract

This work is devoted to interpretation of concepts of Zariski dimension of an algebraic variety over a field and of Krull dimension of a coordinate ring in algebraic geometry over algebraic structures of an arbitrary signature. Proposed dimensions are ordinal numbers (ordinals).

Original languageEnglish
Pages (from-to)1425-1448
Number of pages24
JournalInternational Journal of Algebra and Computation
Volume28
Issue number8
DOIs
StatePublished - 1 Dec 2018

Keywords

  • Krull dimension
  • Partially ordered set
  • Zariski dimension
  • algebraic structure
  • coordinate algebra
  • irreducible algebraic set
  • ordinal number
  • projective dimension
  • radical dimension
  • universal algebraic geometry

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