Geodesic
Exact sequences in the Galois theory of rings
Zapiski Nauchnykh Seminarov POMI, Rings and modules. Part 2, Tome 94 (1979), pp. 104-111

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We study the second and fifth terms of the seven-term exact sequences mentioned in Ref. Zh. Mat. 1978, 6A417. For any (not necessarily separable) ring extension we construct an eight-term exact sequence whose terms are Tate cohomology groups. 
@article{ZNSL_1979_94_a9,
     author = {A. S. Merkur'ev},
     title = {Exact sequences in the {Galois} theory of rings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {104--111},
     publisher = {mathdoc},
     volume = {94},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_94_a9/}
}
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A. S. Merkur'ev. Exact sequences in the Galois theory of rings. Zapiski Nauchnykh Seminarov POMI, Rings and modules. Part 2, Tome 94 (1979), pp. 104-111. http://geodesic.mathdoc.fr/item/ZNSL_1979_94_a9/