On the equationally artinian groups

Mohammad Shahryari, Javad Tayyebi

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we study the property of being equationally Artinian in groups. We define the radical topology corresponding to such groups and investigate the structure of irreducible closed sets of these topologies. We prove that a finite extension of an equationally Artinian group is again equationally Artinian. We also show that a quotient of an equationally Artinian group of the form G[t] by a normal subgroup which is a finite union of radicals, is again equationally Artnian. A necessary and sufficient condition for an Abelian group to be equationally Artinian will be given as the last result. This will provide a large class of examples of equationally Artinian groups.

Original languageEnglish
Pages (from-to)583-595
Number of pages13
JournalJournal of Siberian Federal University - Mathematics and Physics
Volume13
Issue number5
DOIs
Publication statusPublished - 2020

Keywords

  • Algebraic geometry over groups
  • Equationally Artinian groups
  • Equationally Noetherian groups
  • Radical topology
  • Radicals
  • Systems of group equations
  • Zariski topology

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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