Relative Cotorsion Pairs In Abelian Categories

In this thesis,we first study right n-cotorsion pairs in Abelian categories,give the definition of special preenvelopes via right n-cotorsion pairs,and give some relationships between right n-cotorsion pairs and special preenvelopes.Secondly,we study cotorsion pairs relative to a balanced pair,and give the definition of relative n-cotorsion pairs by analogy to the definition of n-cotorsion pairs,and study their properties.Finally,we study Gorenstein flat dimension and restricted flat dimension in the category of modules,and give a new sufficient condition for the Foxby’s conjecture to hold over noncommutative rings.