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The book can be used as a text for graduate students and as a handbook for researchers and specialists. The material in the first three chapters constitute notes from lectures of the authors at their respective universities and is suitable for an introductory course in module and ring theory. The following chapters are suitable for a course in relative homological algebra and its applications to commutative and non-commutative algebra. The last three chapters give applications to ring theory. These chapters together with Chapter 7 contain recent achievements including a solution to the flat cover conjecture.
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