1. PERIODIC SHORT EXACT SEQUENCES AND PERIODIC PURE-EXACT SEQUENCES.
- Author
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BOUCHIBA, SAMIR and KHALOUI, MOSTAFA
- Subjects
- *
MATHEMATICAL sequences , *FINITE groups , *MODULES (Algebra) , *HOMOLOGY theory , *MATHEMATICAL forms , *GORENSTEIN rings , *PROJECTIVE spaces - Abstract
Benson and Goodearl [Periodic flat modules, and flat modules for finite groups, Pacific J. Math.196(1) (2000) 45-67] proved that if M is a flat module over a ring R such that there exists an exact sequence of R-modules 0 → M → P → M → 0 with P a projective module, then M is projective. The main purpose of this paper is to generalize this theorem to any exact sequence of the form 0 → M → G → M → 0, where G is an arbitrary module over R. Moreover, we seek counterpart entities in the Gorenstein homological algebra of pure projective and pure injective modules. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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