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 J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 5, Pages 583–595 (Mi jsfu865)

On the equationally Artinian groups

a Department of Mathematics College of Science Sultan Qaboos University, Muscat, Oman
b Department of Pure Mathematics Faculty of Mathematical Sciences University of Tabriz, Tabriz, Iran

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.

Keywords: algebraic geometry over groups, systems of group equations, radicals, Zariski topology, radical topology, equationally Noetherian groups, equationally Artinian groups.

DOI: https://doi.org/10.17516/1997-1397-2020-13-5-583-595

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UDC: 512.5
Accepted: 16.08.2020
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Citation: Mohammad Shahryari, Javad Tayyebi, “On the equationally Artinian groups”, J. Sib. Fed. Univ. Math. Phys., 13:5 (2020), 583–595

Citation in format AMSBIB
\Bibitem{ShaTay20}
\paper On the equationally Artinian groups
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 5
\pages 583--595
\mathnet{http://mi.mathnet.ru/jsfu865}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-5-583-595}