Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16.10

Retrieve articles in all journals with MSC: 16.10

Additional Information

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