On phi-2-Absorbing phi‎-2-Absorbing Primary Hyperideals of A Multiplicative Hyperring

Mahdi Anbarloei

Abstract


‎Let $R$ be a multiplicative hyperring‎. ‎In this paper‎, ‎we extend the concept of 2-absorbing hyperideals and 2-absorbing primary hyperideals to the context ‎$‎\varphi‎$‎-2-absorbing hyperideals and ‎$‎\varphi‎$‎-2-absorbing primary hyperideals. Let ‎$‎E(R)‎$‎ be the set of hyperideals of ‎$‎R‎$‎‎ and ‎$\varphi : E(R) \longrightarrow E(R) \cup \{\phi\}‎$‎ be a function. A nonzero proper hyperideal ‎$‎I‎$‎ of ‎$‎R‎$‎ is called a ‎$\varphi‎$‎- 2-absorbing hyperideal if for all ‎$x, y, z \in R, xoyoz \subseteq I- \varphi(I)‎$‎ implies
‎$xoy \subseteq I‎$‎ or ‎$‎yoz \subseteq I‎$‎ or ‎$‎xoz \subseteq I‎$‎. Also, a nonzero proper hyperideal ‎$‎I‎$‎ of ‎$‎R‎$‎ is called a ‎$\varphi‎$‎- 2-absorbing primary hyperideal if for all ‎$x, y, z \in R, \ xoyoz \subseteq I- \varphi(I)‎$‎ implies
‎$xoy \subseteq I‎$‎ or ‎$‎yoz \subseteq r(I)‎$‎ or ‎$‎xoz \subseteq r(I)‎$‎. A number of results concerning them are given.

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DOI: https://doi.org/10.22342/jims.25.1.699.35-43

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Journal of the Indonesian Mathematical Society
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p-ISSN: 2086-8952 | e-ISSN: 2460-0245


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