Some results on the 2-absorbing primary hyperideals in multiplicative hyperrings

Document Type : Research Articles

Author

Department of Basic Sciences, Technical and Vocational University(TVU), Tehran, Iran

10.22080/cjms.2025.30043.1774

Abstract

The structural investigation of regular prime ideals
in the setting of multiplicative hyperrings constitutes a profound
and evolving area within hyperstructure theory. This domain not
only enhances the theoretical foundation of hyperalgebra but also
provides a versatile framework for interpreting and generalizing
classical algebraic concepts. By relaxing the conventional binary
operations into hyperoperations, multiplicative hyperrings offer a
rich 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 2-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 prime
ideals and allow us to explore more intricate algebraic phenomena
that are otherwise obscured in the classical setting. The purpose of
this paper is to rigorously explore and characterize the properties of
2-absorbing δ-prime hyperideals in multiplicative hyperrings. We
aim to provide a comprehensive analysis of their defining condi-
tions, structural implications, and potential interactions with other
classes of hyperideals.

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Main Subjects

Caspian Journal of Mathematical Sciences
Volume 15, Issue 1 - Serial Number 29
In progress
2026
Pages 67-77

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