Geodesic
On the equational Artinian algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 875-881

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Equational Artinian algebras were introduced in our previous work: Compactness conditions in universal algebraic geometry, Algebra and Logic, 2016, 55 (2). In this note, we define the notion of radical topology with respect to an algebra $A$ and using the well-known König lemma in graph theory, we show that the algebra $A$ is equational Artinian iff this topology is Noetherian. This completes the analogy between equational Noetherian and equational Artinian algebras.
Keywords: algebraic sets, radical ideals, coordinate algebras, Zariski topology, equationally Noetherian algebras, equational Artinian algebras; radical topology.
Mots-clés : algebraic structures, equations 
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     author = {P. Modabberi and M. Shahryari},
     title = {On the equational {Artinian} algebras},
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P. Modabberi; M. Shahryari. On the equational Artinian algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 875-881. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a23/