NULLSTELLENSATZ FOR RELATIVE EXISTENTIALLY CLOSED GROUPS

Mohammad Shahryari*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that in every variety of G-groups, every G-existentially closed element satisfies nullstellensatz for finite consistent systems of equations. This will generalize Theorem G of [J. Algebra, 219 (1999) 16–79]. As a result we see that every pair of G-existentially closed elements in an arbitrary variety of G-groups generate the same quasi-variety and if both of them are qω-compact, they are geometrically equivalent.

Original languageEnglish
Pages (from-to)125-130
Number of pages6
JournalInternational Journal of Group Theory
Volume11
Issue number2
DOIs
Publication statusPublished - Jun 2022
Externally publishedYes

Keywords

  • Algebraic geometry over groups
  • Existentially closed groups
  • Nullstellensatz
  • Quasi-varieties
  • Varieties of groups

ASJC Scopus subject areas

  • Algebra and Number Theory

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