On the equational artinian algebras

P. Modabberi, M. Shahryari

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)875-881
Number of pages7
JournalSiberian Electronic Mathematical Reports
Volume13
DOIs
Publication statusPublished - 2016
Externally publishedYes

Keywords

  • Algebraic sets
  • Algebraic structures
  • Coordinate algebras
  • Equational artinian algebras
  • Equationally noetherian algebras
  • Equations
  • Radical ideals
  • Radical topology
  • Zariski topology

ASJC Scopus subject areas

  • Mathematics(all)

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