module; inverse polynomial; homological dimensions; Hom; Ext; Tor
In this paper we compute injective, projective and flat dimensions of inverse polynomial modules as $R[x]$-modules. We also generalize Hom and Ext functors of inverse polynomial modules to any submonoid but we show Tor functor of inverse polynomial modules can be generalized only for a symmetric submonoid.
 F. S. Macaulay: The algebraic theory of modular system. Cambridge Tracts in Math. 19 (1916).
 D. G. Northcott: Injective envelopes and inverse polynomials
. J. London Math. Soc. (2), 8 (1974), 290–296. MR 0360555
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