Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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Injective Property Of Generalized Inverse Polynomial Module

  • Published : 2000.04.01
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Abstract

Northcott and Mckerrow proved that if R is a left noe-therian ring and E is an injective left R-module, then E[x-1] is an injective left R[x]-module. In this paper we generalize Northcott and McKerrow's result so that if R is a left noetherian ring and E is an in-jective left R-module, then E[x-S] is an injective left R[xS]-module, where S is a submonoid of N (N is the set of all natural numbers).

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References

  1. Quart J. Math. Oxford v.25 no.3 On the Injective Dimension of Modules of Power Series A. S. McKerrow
  2. Comm. Algebra v.26 Content and Inverse Polynomials on Artinian Modules L. Melkersson
  3. London Math. Soc v.3 no.2 Injective Envelopes and Inverse Polynomials D. G. Northcott
  4. Comm. Algebra v.21 Inverse Polynomials and Injective Covers S. Park
  5. Arch. der Math v.63 The Macaulay-Northcott Functor S. Park