ABSTRACT

There is a discussion of homological dimensions of rings and modules in [146, chapter 6] and [147, chapter 4]. This chapter considers some other questions connected with these notions.

For the reader’s convenience Section 4.1 summarizes the basic concepts and results on projective and injective dimensions of modules, and on the global dimensions of rings. Concepts and results on flat dimensions of modules and weak dimensions of rings are presented in Section 4.2. In Section 4.3 we collect some useful results for calculating global homological dimensions of various classes of rings and present some examples.