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Paper   IPM / M / 15698
School of Mathematics
  Title:   Equivalence of some homological conditions for ring epimorphisms
  Author(s):  Zahra Nazemian (Joint with A. Facchini)
  Status:   Published
  Journal: J. Pure Appl. Algebra
  Year:  2018
  Pages:   DOI: 10.1016/j.jpaa.2018.06.013
  Supported by:  IPM
  Abstract:
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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