English

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.

Keywords

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

R2 v1 2026-06-21T14:50:02.003Z