Projective Approximations
1984 ◽
Vol 36
(1)
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pp. 178-192
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Let R be an associative ring with 1 ≠ 0. Throughout we will be considering unitary left R-modules. Given a chain complex C over R, a free approximation of C is defined to be a free chain complex F over R together with an epimorphism τ:F → C of chain complexes with the property that H(τ):H(F) ≃ H(C). In Chapter 5, Section 2 of [3] it is proved that any chain complex C over Z has a free approximation τ:F → C. Moreover given a free approximation τ:F → C of C and any chain map f:F’ → C with F’ a free chain complex over Z, there exists a chain map φ:F’→ F with T O φ = f . Any two chain maps φ, ψ of F’ in F with T O φ = T O ψ are chain homotopic.
2009 ◽
Vol 18
(09)
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pp. 1227-1258
Keyword(s):
2020 ◽
Vol 4
(4)
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pp. 455-480
2013 ◽
Vol 29
(0)
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pp. 21-22
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2019 ◽
Vol 150
(4)
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pp. 1937-1964
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Keyword(s):
2012 ◽
Vol 55
(1)
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pp. 145-160
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