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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Isomorphic polynomial rings

Authors: D. B. Coleman and E. E. Enochs
Journal: Proc. Amer. Math. Soc. 27 (1971), 247-252
MSC: Primary 16.10
MathSciNet review: 0272805
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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.

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Keywords: Polynomial ring, group of units, Artinian ring, locally nilpotent ideal, left $ T$-nilpotent ideal, Jacobson radical, left perfect ring
Article copyright: © Copyright 1971 American Mathematical Society

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