Bulletin of the Korean Mathematical Society (대한수학회보)

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PRIMARY DECOMPOSITION OF SUBMODULES OF A FREE MODULE OF FINITE RANK OVER A BÉZOUT DOMAIN

  • Fatemeh Mirzaei (Department of Pure Mathematics Mahani Mathematical Research Center Shahid Bahonar University of Kerman) ;
  • Reza Nekooei (Department of Pure Mathematics Mahani Mathematical Research Center Shahid Bahonar University of Kerman)
  • Received : 2022.03.26
  • Accepted : 2022.10.11
  • Published : 2023.03.31
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Abstract

Let R be a commutative ring with identity. In this paper, we characterize the prime submodules of a free R-module F of finite rank with at most n generators, when R is a GCD domain. Also, we show that if R is a Bézout domain, then every prime submodule with n generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of F over a Bézout domain and characterize the minimal primary decomposition of this submodule.

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Acknowledgement

The authors would like to thank the referee for his/her useful suggestions that improved the presentation of this paper. The authors acknowledge support from the Iran National Science Foundation: INSF.

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