International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 256267, 13 pages
doi:10.1155/2010/256267
Research Article

On Presented Dimensions of Modules and Rings

Dexu Zhou1 and Zhiwei Gong2

1Department of Mathematics, Fujian Normal University, Fuzhou 350007, China
2College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, China

Received 21 August 2009; Accepted 12 March 2010

Academic Editor: Francois Goichot

Copyright © 2010 Dexu Zhou and Zhiwei Gong. 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 define the presented dimensions for modules and rings to measure how far away a module is from having an infinite finite presentation and develop ways to compute the projective dimension of a module with a finite presented dimension and the right global dimension of a ring. We also make a comparison of the right global dimension, the weak global dimension, and the presented dimension and divide rings into four classes according to these dimensions.