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

Peng Xu; Melis Bolat; Elif Kaya; Serkan Onar; Bayram Ali Ersoy; Kostaq Hila

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arXiv · 2110.10264

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

Peng Xu·Melis Bolat·Elif Kaya·Serkan Onar·Bayram Ali Ersoy·Kostaq Hila

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Abstract

In this study, we examine some properties of $r$-hyperideals in the 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 is also an $r$-hyperideal. We also introduce a generalization of r-hyperideals and we prove some properties of them.

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Peng Xu, Melis Bolat, Elif Kaya, Serkan Onar, Bayram Ali Ersoy, Kostaq Hila. 2021-10-19. $r$-Hyperideals and Generalizations of $r$-Hyperideals in Krasner Hyperrings. https://arxiv.org/abs/2110.10264

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