On the Equational Artinian Algebras

Abstract

Equational Artinian algebras were introduced in our previous work: {\em Equational conditions in universal algebraic geometry, to appear in Algebra and Logic, 2015}. In this note, we define the notion of {\em radical topology with respect to an algebra $A$} and using the well-known König lemma in graph theory, we show that the algebra $A$ is equational Artinian iff this topology is noetherian. This completes the analogy between equational noetherian and equational Artinian algebras.

10 pages, a theorem on ultrapowers is added. arXiv admin note: substantial text overlap with arXiv:1401.4389

References in corpus (1)

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

Cited by in corpus (1)

• On the equationally Artinian groups