International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 20, Pages 3261-3268
doi:10.1155/IJMMS.2005.3261

On pairs of subrings with a common set of proper ideals

Yasuyuki Hirano1 and Hisaya Tsutsui2,3

1Department of Mathematics, Okayama University, Okayama 700-8530, Japan
2Department of Mathematics, Embry-Riddle Aeronautical University, Prescott 86301, AZ, USA
3Department of Mathematics, Millersville University, Millersville 17551, PA, USA

Received 5 July 2005

Copyright © 2005 Yasuyuki Hirano and Hisaya Tsutsui. 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

A study of pairs of commutative rings with the same set of prime ideals appears in the literature. In this paper, we investigate pairs of subrings, not necessarily commutative, with a common set of proper ideals.