A noncommutative Hilbert basis theorem and subrings of matrices
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- by S. A. Amitsur PDF
- Trans. Amer. Math. Soc. 149 (1970), 133-142 Request permission
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.References
- 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, DOI 10.1007/BF02413733
- Claudio Procesi, Non-commutative affine rings, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 8 (1967), 237–255 (English, with Italian summary). MR 224657
Additional Information
- © Copyright 1970 American Mathematical Society
- 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