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| Paper IPM / M / 15698 |
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| Abstract: | |
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Let R be a right and left Ore ring, S its set of regular elements and Q = R[S−1] = [S−1] R the classical ring of quotients of R. We prove that if \Fdim(QQ) = 0, then
the following conditions are equivalent:
(i) Flat right
R-modules are strongly flat.
(ii) Matlis-cotorsion right R-modules are Enochs-cotorsion.
(iii) h-divisible right R-modules are weak-injective.
(iv) Homomorphic images of weak-injective right R-modules are weak-injective.
(v) Homomorphic images of injective right R-modules are weak-injective.
(vi) Right R-modules of weak dimension ≤ 1 are of projective dimension ≤ 1.
(vii) The cotorsion pairs (\Cal P1,\Cal D) and (\Cal F1,\Cal W\Cal I) coincide.
(viii) Divisible right R-modules are weak-injective. This extends a result by Fuchs and Salce (2018) [10] for modules over a commutative ring R.
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