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All Modules Have Flat Covers
Author(s) -
Bican L.,
El Bashir R.,
Enochs E.
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1017/s0024609301008104
Subject(s) - mathematical proof , mathematics , cover (algebra) , conjecture , set (abstract data type) , calculus (dental) , pure mathematics , algebra over a field , geometry , computer science , programming language , engineering , mechanical engineering , medicine , dentistry
In this paper we give two different proofs that the flat cover conjecture is true: that is, every module has a flat cover. The two proofs are of completely different nature, and, we hope, will have different applications. The first of the two proofs (due to the third author) is essentially an application of the work of P. Eklof and J. Trlifaj (work which is more set‐theoretic). The second proof (due to the first two authors) is more direct, and has a model‐theoretic flavour.