This article is cited in 6 papers

Equational conditions in universal algebraic geometry

P. Modabberi, M. Shahryari

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

Abstract: 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.

Keywords: algebraic structures, equations, 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, equational domains, Hilbert's basis theorem.

UDC: 512.54.0+512.57

Received: 31.01.2014
Revised: 03.10.2015

DOI: 10.17377/alglog.2016.55.204

 English version: Algebra and Logic, 2016, 55:2, 146–172

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