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.
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.