This article is cited in 2 papers

Mathematical logic, algebra and number theory

On the equational Artinian algebras

P. Modabberi, M. Shahryari

Department of Pure Mathematics, University of Tabriz, Tabriz, Iran

Abstract: Equational Artinian algebras were introduced in our previous work: Compactness conditions in universal algebraic geometry, Algebra and Logic, 2016, 55 (2). In this note, we define the notion of 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.

Keywords: algebraic structures, equations, algebraic sets, radical ideals, coordinate algebras, Zariski topology, equationally Noetherian algebras, equational Artinian algebras; radical topology.

UDC: 512.71+512.55

MSC: 03C99,08A99,14A99

Received February 29, 2016, published October 14, 2016

Language: English

DOI: 10.17377/semi.2016.13.069

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