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

By E. Daniyarova, Alexei G. Myasnikov, Vladimir Nikanorovich Remeslennikov. 2010

50 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f47c819b226f219ae1b79daf2e25f71816c29b6

Citations in the corpus

• Algebraic geometry over algebraic structures. II. Foundations (2012, unknown): “In the nearest future, we plan to publish the papers “Equationally Noetherian property and compactness” [19] and “Equational domains and co-domains” [20] along this series.”