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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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: A finitely generated central extension $ A[{u_1}, \ldots ,{u_k}]$ of a commutative noetherian ring A, satisfies the ascending chain condition for ideals P for which $ A[{u_1}, \ldots ,{u_k}]/P$ can be embedded in matrix rings $ {M_n}(K)$ 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 $ {M_n}(K)$ but nevertheless cannot be embedded in any matrix ring over a commutative ring of arbitrary finite order.


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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