Torsion theories over semihereditary rings

Journal of the Australian Mathematical Society

M. W. Evans¹ 

关键词: 16 A 08;    16 A 14;    16 A 52;   

DOI  :  10.1017/S1446788700026495

学科分类：数学（综合）

来源: Cambridge University Press

【 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, ℱ) 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 “flat” homomorphisms. A class of prime torsion theories is introduced which determines the torsion theory (G, ℱG). The torsion theory (JG, ℱG) is used to find a suitable generalisation of Dedekind Domain.

【 授权许可】

Unknown