Table of Contents
ISRN Algebra
Volume 2011 (2011), Article ID 497831, 6 pages
http://dx.doi.org/10.5402/2011/497831
Research Article

(Weak) Gorenstein Global Dimension of Semiartinian Rings

Department of Mathematics, Faculty of Science and Technology of Fez, University S.M. Ben Abdellah Fez, Morocco

Received 18 April 2011; Accepted 20 May 2011

Academic Editors: A. Jaballah and D. Kressner

Copyright © 2011 Mohammed Tamekkante and Mohamed Chhiti. 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 prove that if 𝑅 is a semiartinian commutative ring, the Gorenstein global dimension of 𝑅 equals the supremum of the Gorenstein projective and injective dimensions of simple 𝑅 -modules, and the weak Gorenstein global dimension of 𝑅 equals the supremum of the Gorenstein flat dimensions of simple 𝑅 -modules.