Some results on the ۲-absorbing primary hyperideals in multiplicative hyperrings

The structural investigation of regular prime idealsin the setting of multiplicative hyperrings constitutes a profoundand evolving area within hyperstructure theory. This domain notonly enhances the theoretical foundation of hyperalgebra but alsoprovides a versatile framework for interpreting and generalizingclassical algebraic concepts. By relaxing the conventional binaryoperations into hyperoperations, multiplicative hyperrings offer arich algebraic environment where classical notions such as ideals,prime ideals, and their generalizations acquire novel and meaning-ful forms. In particular, the study of generalized prime-like objects-such as ۲-absorbing δ-prime hyperideals-plays a central role in deep-ening our comprehension of the internal behavior of hyperrings.These generalized structures extend the traditional notion of primeideals and allow us to explore more intricate algebraic phenomenathat are otherwise obscured in the classical setting. The purpose ofthis paper is to rigorously explore and characterize the properties of۲-absorbing δ-prime hyperideals in multiplicative hyperrings. Weaim to provide a comprehensive analysis of their defining condi-tions, structural implications, and potential interactions with otherclasses of hyperideals.

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Keywords: Hyperrings ، Hyperideals ، δ-Prime Hyper- ideals