On the Equational Artinian Algebras
Copyright policy )On the Equational Artinian Algebras
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 K��nig 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
equational Artinian algebras, radical topology, radical ideals, Generalizations (algebraic spaces, stacks), Equational compactness, Mathematics - Logic, Group Theory (math.GR), Primary 03C99, Secondary 08A99, 14A99, algebraic structures, coordinate algebras, algebraic sets, equationally Noetherian algebras, equations, Equational classes, universal algebra in model theory, FOS: Mathematics, Zariski topology, Logic (math.LO), Mathematics - Group Theory
equational Artinian algebras, radical topology, radical ideals, Generalizations (algebraic spaces, stacks), Equational compactness, Mathematics - Logic, Group Theory (math.GR), Primary 03C99, Secondary 08A99, 14A99, algebraic structures, coordinate algebras, algebraic sets, equationally Noetherian algebras, equations, Equational classes, universal algebra in model theory, FOS: Mathematics, Zariski topology, Logic (math.LO), Mathematics - Group Theory
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