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PERIODIC SHORT EXACT SEQUENCES AND PERIODIC PURE-EXACT SEQUENCES

SAMIR BOUCHIBA

Department of Mathematics, University Moulay Ismail, Meknes 50000, Morocco

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and

MOSTAFA KHALOUI

Department of Mathematics, University Moulay Ismail, Meknes 50000, Morocco

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https://doi.org/10.1142/S021949881000421XCited by:4 (Source: Crossref)

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.

Keywords:

AMSC: 13D02, 13D05, 13D07, 16E05, 16E10

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