Geodesic
Equational conditions in universal algebraic geometry
Algebra i logika, Tome 55 (2016) no. 2, pp. 219-256.

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Different types of compactness in the Zariski topology are explored: for instance, being equational Noetherian, being equational Artinian, $q_\omega$- and $u_\omega$-compactness. Moreover, general results on the Zariski topology over algebras and groups are proved.
Mots-clés : algebraic structures, equations, equational domains
Keywords: algebraic sets, radical ideal, coordinate algebra, Zariski topology, equationally Noetherian algebras, $q_\omega$-compactness, $u_\omega$-compactness, metacompact algebras, metacompact spaces, equationally Artinian algebras, prevarieties, varieties, free algebras, Hilbert's basis theorem. 
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P. Modabberi; M. Shahryari. Equational conditions in universal algebraic geometry. Algebra i logika, Tome 55 (2016) no. 2, pp. 219-256. http://geodesic.mathdoc.fr/item/AL_2016_55_2_a3/

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