Geodesic
On the equationally Artinian groups
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 583-595

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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. 
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Mohammad Shahryari; Javad Tayyebi. On the equationally Artinian groups. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 583-595. http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a6/