Projective Approximations

Varadarajan, K.

Canadian journal of mathematics, Tome 36 (1984) no. 1, pp. 178-192

Résumé

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.

Détail

DOI : 10.4153/CJM-1984-012-7

Bibliographie

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