Isomorphic polynomial rings
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- by D. B. Coleman and E. E. Enochs
- Proc. Amer. Math. Soc. 27 (1971), 247-252
- DOI: https://doi.org/10.1090/S0002-9939-1971-0272805-3
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Abstract:
A ring is called invariant if whenever $B$ is a ring such that the polynomial rings $A[X]$ and $B[X]$ are isomorphic, then $A$ and $B$ are isomorphic. $A$ is strongly invariant if an isomorphism $A[X] \to B[X]$ maps $X$ onto a $B$-generator of $B[X]$. Strongly invariant rings are invariant. Among the strongly invariants are left perfect rings, local domains and rings of algebraic integers.References
- S. A. Amitsur, Radicals of polynomial rings, Canadian J. Math. 8 (1956), 355–361. MR 78345, DOI 10.4153/CJM-1956-040-9
- Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488. MR 157984, DOI 10.1090/S0002-9947-1960-0157984-8
- Robert W. Gilmer Jr., $R$-automorphisms of $R[X]$, Proc. London Math. Soc. (3) 18 (1968), 328–336. MR 229633, DOI 10.1112/plms/s3-18.2.328
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 247-252
- MSC: Primary 16.10
- DOI: https://doi.org/10.1090/S0002-9939-1971-0272805-3
- MathSciNet review: 0272805