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- W2052432468 abstract "Abstract Hattori (1960) defined a right R -module A to be torsion-free if for all a ∈ A and x ∈ R , ax = 0 implies that there exist elements {x 1 , x 2 , …, x n } ⊆ R with x i x = 0 for all 1 ≦ i ≦ n and {a 1 , a 2 , …, a n } ⊆ A such that a = a i x i . Left torsion-free is defined similarly. It is shown that for a ring R , these torsion-free modules are the torsion-free class of a hereditary torsion theory, corresponding to a perfect topology, if and only if the left flat epimorphic hull of R is a regular ring which is both left and right torsion-free. A class of right semi-hereditary rings for which the torsion-free modules of Hattori satisfy the above property are found and this class of rings is discussed." @default.
- W2052432468 created "2016-06-24" @default.
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- W2052432468 date "1977-05-01" @default.
- W2052432468 modified "2023-09-25" @default.
- W2052432468 title "Extensions of semi-hereditary rings" @default.
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- W2052432468 doi "https://doi.org/10.1017/s1446788700018954" @default.
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