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

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

2010-02-23

arxiv.org/abs/1002.4243v2

Mathematics

Algebraic Geometry

46 pages; 2 figures

Scientific paper

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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