Abstract
In this paper we compute injective, projective and flat dimensions of inverse polynomial modules as \(R\left[ x \right]\)-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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. S. Macaulay: The algebraic theory ofm odular system. Cambridge Tracts in Math. 19 (1916).
H. Matsumura: Commutative Algebra. W.A. Benjamin, Inc., New York, 1970.
A. S. McKerrow: On the injective dimension ofm odules of power series. Quart J. Math. Oxford Ser. (2), 25 (1974), 359–368.
D. G. Northcott: Injective envelopes and inverse polynomials. J. London Math. Soc. (2), 8 (1974), 290–296.
S. Park: Inverse polynomials and injective covers. Comm. Algebra 21 (1993), 4599–4613.
S. Park: The Macaulay-Northcott functor. Arch. Math. (Basel) 63 (1994), 225–230.
J. Rotman: An Introduction to Homological Algebra. Academic Press Inc., New York, 1979.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Park, S. The General Structure of Inverse Polynomial Modules. Czechoslovak Mathematical Journal 51, 343–349 (2001). https://doi.org/10.1023/A:1013798914813
Issue Date:
DOI: https://doi.org/10.1023/A:1013798914813