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arXiv · 1506.00090

On the Equational Artinian Algebras

P. Modabberi·M. Shahryari
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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 K\"onig 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.

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P. Modabberi, M. Shahryari. 2015-05-30. On the Equational Artinian Algebras. https://arxiv.org/abs/1506.00090

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