Geodesic
On a~criterion of exactness of a~finite free complex
Matematičeskie zametki, Tome 17 (1975) no. 5, pp. 711-716.

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In this paper we prove the sufficiency of a criterion of exactness of a complex of finitely generated free modules over a commutative ring, which was known earlier for the case of a complex over a Noetherian ring. 
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     author = {V. V. Schechtman},
     title = {On a~criterion of exactness of a~finite free complex},
     journal = {Matemati\v{c}eskie zametki},
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V. V. Schechtman. On a~criterion of exactness of a~finite free complex. Matematičeskie zametki, Tome 17 (1975) no. 5, pp. 711-716. http://geodesic.mathdoc.fr/item/MZM_1975_17_5_a3/