Modules with local finite BIB-ranks and Grothendieck groups of some categories

For a commutative semilocal ring R, a remarkable property is that if P is a finitely generated projective R-module with constant rank, then P is free. In this paper, firstly, we extend the above result to the general case (not necessarily commutative). Secondly, we consider the Grothendieck groups o...

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Bibliographic Details
Published in:	Quaestiones mathematicae Vol. 37; no. 1; pp. 91 - 109
Main Author:	Zhu, Xiaosheng
Format:	Journal Article
Language:	English
Published:	Grahamstown Taylor & Francis 02-01-2014 Taylor & Francis Ltd
Subjects:	Grothendieck groups local finite BIB-ranks local power stably free Semilocal ring
Online Access:	Get full text
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Summary:	For a commutative semilocal ring R, a remarkable property is that if P is a finitely generated projective R-module with constant rank, then P is free. In this paper, firstly, we extend the above result to the general case (not necessarily commutative). Secondly, we consider the Grothendieck groups of some subcategories of the category of finitely generated projective modules and obtain some exact sequences of K-groups. Finally, we give some applications of the above Grothendieck groups.
ISSN:	1607-3606 1727-933X
DOI:	10.2989/16073606.2013.779956