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On an ”arithmetical” functor. (English. Russian original) Zbl 0575.18007
Math. USSR, Sb. 50, 533-538 (1985); translation from Mat. Sb., Nov. Ser. 122 (164), No. 4, 546-551 (1983).
It is shown that for the values of \(\widehat{\text{Tor}}^ k(M,N)\) to be noetherian it suffices that all five arguments be noetherian (the ground ring, the local algebras over it, and the modules over these).
MSC:
18G15 Ext and Tor, generalizations, K√ľnneth formula (category-theoretic aspects)
13D99 Homological methods in commutative ring theory
13E05 Commutative Noetherian rings and modules
Keywords:
Tor; noetherianness
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