ABSTRACT
Chapter 19 The Cotorsion Dimension of Modules and Rings Lixin Mao Department of Basic Courses, Nanjing Institute of Technology, Nanjing 210013, Peoples Republic of China Department of Mathematics, Nanjing University, Nanjing 210093, Peoples Republic of China maolx2@hotmail.com
Nanqing Ding Department of Mathematics, Nanjing University, Nanjing 210093, Peoples Republic of China nqding@nju.edu.cn
19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19.2 General Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 19.3 Cotorsion Dimension under Change of Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 19.4 Applications in Commutative Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
Abstract In this paper, we introduce a dimension, called the cotorsion dimension, for modules and rings. The relations between the cotorsion dimension and other dimensions are discussed. Various results are developed, some extending known results. Keywords: Cotorsion dimension; Cotorsion envelope; Flat cover; Perfect ring.
