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r-Hyperideals and Generalizations of r-Hyperideals in Krasner Hyperrings

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  • Peng Xu
  • Melis Bolat
  • Elif Kaya
  • Serkan Onar
  • Bayram Ali Ersoy
  • Kostaq Hila
  • Kamal Kumar

Abstract

This paper deals with Krasner hyperrings as an important class of algebraic hyperstructures. We investigate some properties of r-hyperideals in commutative Krasner hyperrings. Some properties of pr-hyperideals are also studied. The relation between prime hyperideals and r-hyperideals is investigated. We show that the image and the inverse image of an r-hyperideal are also an r-hyperideal. We also introduce a generalization of r-hyperideals, and we prove some properties of them.

Suggested Citation

  • Peng Xu & Melis Bolat & Elif Kaya & Serkan Onar & Bayram Ali Ersoy & Kostaq Hila & Kamal Kumar, 2022. "r-Hyperideals and Generalizations of r-Hyperideals in Krasner Hyperrings," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-10, July.
    • Handle: RePEc:hin:jnlmpe:7862425
    DOI: 10.1155/2022/7862425
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