Torsion theories over semihereditary rings

摘要

In this paper the class of rings for which the right flat modules form the torsion-free class of a hereditary torsion theory (G, a?±) are characterized and their structure investigated. These rings are called extended semihereditary rings. It is shown that the class of regular rings with ring homomorphism is a full co-reflective subcategory of the class of extended semihereditary rings with a€?flata€? homomorphisms. A class of prime torsion theories is introduced which determines the torsion theory (G, a?±G). The torsion theory (JG, a?±G) is used to find a suitable generalisation of Dedekind Domain.