On Bernstein Algebras Satisfying Chain Conditions |
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| Authors: | Nadia Boudi Fouad Zitan |
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| Affiliation: | 1. University Moulay Ismail, Faculty of Sciences, Department of Mathematics and Informatics , Beni M'Hamed, Meknes, Morocco boudi@yahoo.ca;3. University Abdelmalek Essaadi, Faculty of Sciences, Department of Mathematics and Informatics , Tétouan, Morocco |
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| Abstract: | Our aim in this article is to study Noetherian and Artinian Bernstein algebras. We show that for Bernstein algebras which are either Jordan or nuclear, each of the Noetherian and Artinian conditions implies finite dimensionality. This result fails for general Noetherian or Artinian Bernstein algebras. We also investigate the relationships between the three finiteness conditions: Noetherian, Artinian, and finitely generated. Especially, we prove that Noetherian Bernstein algebras are finitely generated. |
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| Keywords: | Artinian algebras Artinian modules Bernstein algebras Noetherian algebras |
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