Abstract

We investigate the structure of pure-syzygy modules in a pure-projective resolution of any right R-module over an associative ring R with an identity element. We show that a right R-module M is pure-projective if and only if there exists an integer n ≥ 0 and a pure-exact sequence 0 → M → P_n →⋯ → P₀ → M → 0 with pure-projective modules P_n,…,P₀. As a consequence we get the following version of a result in Benson and Goodearl, 2000: A flat module M is projective if M admits an exact sequence 0 → M → F_n →⋯ → F₀ → M → 0 with projective modules F_n,…,F₀.

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