Summary
In this paper we give a non commutative analogue of the Krull-Akizuki theorem, precisely:If R=A[x 1,...,xm] is a finitely generated P. I. algebra over a commutative noetherian ring, then the three conditions are equivalent:
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1)
R is right artinian.
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2)
R is left artinian.
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3)
Every prime ideal of R is maximal.
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Bibliografia
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C. Procesi,Non commutative Jacobson rings, Annali Scuola Norm. Sup. Pisa, v. XXI, f. II, (1967), pp. 381–390.
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Procesi, C. Sugli anelli non commutativi zero dimensionali con identità polinomiale. Rend. Circ. Mat. Palermo 17, 5–12 (1968). https://doi.org/10.1007/BF02849545
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DOI: https://doi.org/10.1007/BF02849545