•  
  •  
 

Keywords

generalized inverse, minus partial order, matrices over commutative ring, projective module, rank– function, dimension–function

Abstract

In this paper, we invoke theory of generalized inverses and minus partial order on regular matrices over a commutative ring to define rank–function for regular matrices and dimension–function for finitely generated projective modules which are direct summands of a free module. Some properties held by the rank of a matrix and the dimension of a vector space over a field are generalized. Also, a generalization of rank-nullity theorem has been established when the matrix given is regular.

Share

COinS
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.