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Jacobson - rings and hilbert algebras with polynomial identities

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Summary

We consider n-tuples of m × m matrices as zeroes of non-commutative polynomials in n-variables and establish an analogue of the classical Hilbert-Nullstellensatz. We study then finitely generated non-commutative algebras over Jacobson rings and obtain results conpletely analogous with the commutative tehory.

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Additional information

In memory of Guido Castelnuovo, in the recurrence of the first centenary of his birth.

Done partly under NSF Senior Foreign Scientist Fellowship at the Univ. of Chicago.

The second named author has been supported by an A.R.O. grant no DA-ARO-D-31-124-G 501 at the Univ. of Chicago.

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Amitsur, S.A., Procesi, C. Jacobson - rings and hilbert algebras with polynomial identities. Annali di Matematica 71, 61–72 (1966) doi:10.1007/BF02413733

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Keywords

  • Polynomial Identity
  • Hilbert Algebra
  • Jacobson Ring