Bulletin of the Korean Mathematical Society (대한수학회보)

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SOME RESULTS ON INTEGER-VALUED POLYNOMIALS OVER MODULES

  • Received : 2019.09.19
  • Accepted : 2020.03.26
  • Published : 2020.09.30
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Abstract

Let M be a module over a commutative ring R. In this paper, we study Int(R, M), the module of integer-valued polynomials on M over R, and IntM(R), the ring of integer-valued polynomials on R over M. We establish some properties of Krull dimensions of Int(R, M) and IntM(R). We also determine when Int(R, M) and IntM(R) are nontrivial. Among the other results, it is shown that Int(ℤ, M) is not Noetherian module over IntM(ℤ) ∩ Int(ℤ), where M is a finitely generated ℤ-module.

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Acknowledgement

The authors are deeply grateful to the referees for helpful comments and for suggesting what became Theorem 3.6. This work has been financially supported by the research deputy of Shahrekord University. The grant number was 98GRD30M531.

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