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 language | English |
|---|---|
| Pages (from-to) | 875-881 |
| Number of pages | 7 |
| Journal | Siberian Electronic Mathematical Reports |
| Volume | 13 |
| DOIs | |
| Publication status | Published - 2016 |
| Externally published | Yes |
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)