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Pure-periodic modules
and a structure of pure-projective resolutions
Daniel Simson |
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Vol. 207 (2002), No. 1, 235–256
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Abstract |
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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 → Pn →⋯ → P0 → M → 0 with pure-projective modules Pn,…,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 → Fn →⋯ → F0 → M → 0 with projective modules Fn,…,F0. |
Milestones
Received: 12 February 2001
Revised: 26 February 2002
Published: 1 November 2002
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Authors |
| Daniel Simson | |
| Faculty of Mathematics and
Informatics Nicholas Copernicus University ul. Chopina 12/18 87-100 Toruń, Poland |
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