The Macaulay-Northcott functor (Q1337774)

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 \textit{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 \(\text{Tor}_ i^{R[x]} (M[x^{-1}], N[x^{-1}]) \cong \text{Tor}^ R_{i-1} (M,N) [x^{- 1}]\).