Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness
Algebraic Geometry
2010-05-20 v2 Logic
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.
Cite
@article{arxiv.1002.4243,
title = {Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness},
author = {Evelina Daniyarova and Alexei Myasnikov and Vladimir Remeslennikov},
journal= {arXiv preprint arXiv:1002.4243},
year = {2010}
}
Comments
46 pages; 2 figures