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S-NOETHERIAN IN BI-AMALGAMATIONS

  • Kim, Hwankoo (Division of Computer Engineering Hoseo University) ;
  • Mahdou, Najib (Laboratory of Modeling and Mathematical Structures Department of Mathematics Faculty of Science and Technology of Fez) ;
  • Zahir, Youssef (Department of Mathematics Faculty of Sciences of Rabat, Mohammed-V University in Rabat)
  • Received : 2020.09.14
  • Accepted : 2021.03.12
  • Published : 2021.07.31
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Abstract

This paper establishes necessary and sufficient conditions for a bi-amalgamation to inherit the S-Noetherian property. The new results compare to previous works carried on various settings of duplications and amalgamations, and capitalize on recent results on bi-amalgamations. Our results allow us to construct new and original examples of rings satisfying the S-Noetherian property.

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Acknowledgement

The authors would like to express their sincere thanks for the referee for his/her careful reading and helpful comments, which have greatly improved this paper.

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