Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness

2010/02/23 by Daniyarova, Evelina, Myasnikov, Alexei, Remeslennikov, Vladimir · 1 citation
#03C05 #08B05 #14A99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1002.4243

Abstract

In this paper we discuss some special generalizations of equationally Noetherian property which naturally arise in the universal algebraic geometry. We introduce weakly equationally Noetherian, qw-compact, uw-compact, and weakly uw-compact algebras and then examine properties of such algebras. Also we consider the connections between five classes: the class of equationally Noetherian algebras, the class of weakly equationally Noetherian algebras, the class of uw-compact algebras, the class of weakly uw-compact algebras, and the class of qw-compact algebras.

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