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

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Xu P., Bolat M., Kaya E., Onar S., Ersoy B. A., Hila K.

MATHEMATICAL PROBLEMS IN ENGINEERING, vol.2022, pp.1-10, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2022
  • Publication Date: 2022
  • Doi Number: 10.1155/2022/7862425
  • Journal Name: MATHEMATICAL PROBLEMS IN ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.1-10
  • Yıldız Technical University Affiliated: Yes

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.