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International Journal of Mathematics and Mathematical Sciences
Volume 2015, Article ID 938648, 3 pages
http://dx.doi.org/10.1155/2015/938648
Research Article

A Direct Proof of a Theorem concerning Treed Overrings

Faculty of Science, Sana’a University, P.O. Box 12460, Sana’a, Yemen

Received 15 April 2015; Accepted 23 June 2015

Academic Editor: David E. Dobbs

Copyright © 2015 Ahmed Ayache. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We improve and provide a direct proof of a theorem that answered a question by Dobbs about treed overrings. More precisely, we show that if is an integrally closed local domain and each of its proper overrings is treed, then is a valuation domain or is a PVD with associated valuation overring such that .