REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: In this talk we will study the classes of modules and chain complexes over a ring R whose Gorenstein-flat dimension is bounded by a positive integer r. We will show that this class is the left half of a complete cotorsion pair in the case R is a Gorenstein ring, by considering a restricted definition of pure submodules, and, in the case of chain complexes, by using a slightly modified definition of cotorsion pairs. We will obtain from these pairs model structures on modules and chain complexes, and will see the relationship between the former and a model structure on chain complexes obtained from the class of modules with flat dimension at most r.