A noncommutative Hilbert basis theorem and subrings of matrices
Author:
S. A. Amitsur
Journal:
Trans. Amer. Math. Soc. 149 (1970), 133-142
MSC:
Primary 16.25
DOI:
https://doi.org/10.1090/S0002-9947-1970-0258869-5
MathSciNet review:
0258869
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Abstract | References | Similar Articles | Additional Information
Abstract: A finitely generated central extension of a commutative noetherian ring A, satisfies the ascending chain condition for ideals P for which
can be embedded in matrix rings
over arbitrary commutative rings K and n bounded. The method of proof leads to an example of a ring R which satisfies the same identities of
but nevertheless cannot be embedded in any matrix ring over a commutative ring of arbitrary finite order.
- [1] S. A. Amitsur and C. Procesi, Jacobson-rings and Hilbert algebras with polynomial identities, Ann. Mat. Pura Appl. (4) 71 (1966), 61–72. MR 206044, https://doi.org/10.1007/BF02413733
- [2] Claudio Procesi, Non-commutative affine rings, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. I (8) 8 (1967), 237–255 (English, with Italian summary). MR 0224657
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1970-0258869-5
Keywords:
Hilbbert basis theorem,
generic matrices,
ascending chain condition,
finitely generated rings with identities
Article copyright:
© Copyright 1970
American Mathematical Society