![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
In this paper, we define the power stably free dimension for rings. Using its relations with other dimensions, we get a classification of rings. Moreover, we give the equivalent characterizations of a ring with power stably free dimension 0, 1 respectively.
For a commutative ring R in which each f. g. module has a finite power stably free dimension, we show that R[x 1, …, xn ] is connected and all f. g. projective modules over R[x 1, …, xn ] are power free.
ACKNOWLEDGMENT
The author heartily thanks the referee for a careful reading of this paper. His valuable comments and suggestions have led to various improvements in my paper. In addition, the author also would like to thank professors T. Y. Lam and W. V. Vasconcelos for their help and encouragement. Supported in part by Chinese Ministry of Education and National Natural Science Foundation of China.