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)



On valuation rings that contain zero divisors

Author: James A. Huckaba
Journal: Proc. Amer. Math. Soc. 40 (1973), 9-15
MSC: Primary 13F05
MathSciNet review: 0318134
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ R$ be a commutative ring with identity. A new proof is given of the theorem due to Samuel and Griffin which states that $ R$ is integrally closed in its total quotient ring if and only if $ R$ is the intersection of $ B$-valuation rings. We then prove the main result of the paper: If $ K$ is a $ \pi $-regular ring, then $ K$ admits only Prüfer rings as valuation rings.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13F05

Retrieve articles in all journals with MSC: 13F05

Additional Information

Keywords: Commutative rings with zero divisors, valuation ring, Prüfer ring, von Neumann regular ring, integral closure of a ring
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society