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The Macaulay-Northcott functor. (English) Zbl 0804.18009

Northcott considered the module \(K[x^{-1}]\) of “inverse polynomials” over the polynomial ring \(K[x]\) (with \(K\) a field). This construction was generalized by A. S. McKerrow [Q. J. Math., Oxf. II. Ser. 25, 359- 368 (1974; Zbl 0302.16027)]. In this paper we consider these generalized inverse polynomial modules and consider their behavior when we apply the usual derived functors. Perhaps the most interesting result is the dimension shift in the natural isomorphism \(\text{Tor}_ i^{R[x]} (M[x^{-1}], N[x^{-1}]) \cong \text{Tor}^ R_{i-1} (M,N) [x^{- 1}]\).
Reviewer: S.Park (Lexington)

MSC:

18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)
18G10 Resolutions; derived functors (category-theoretic aspects)
13F25 Formal power series rings

Citations:

Zbl 0302.16027
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References:

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