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October 27, 2025Open Access

The Direct Product of Hypermodules over a Hyperring

Key Points

The direct product maintains the axioms of R-hypermodules, ensuring structural integrity.
It demonstrates that the direct product functions effectively within the framework of hypermodule theory.
Canonical projections can be interpreted as hyperhomomorphisms in this context.
The extension of classical constructions to hypermodules supports broader applications in algebraic structures.

Abstract

The purpose of this work is studying the direct product of hypermodules. We introduce a general definition of the direct product of R-hypermodules by extending the classical coordinatewise construction from module theory. It is shown that the direct product preserves the axioms of an R-hypermodule. This result helped us to prove that, direct Product of R-hypermodules is an R-hypermodule, and that the canonical projections as hyperhomomorphisms.

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Cite This Study

Yasser AbouElwan (Sat,) studied this question.

synapsesocial.com/papers/68ff87e2c8c50a61f2bdd117 https://doi.org/https://doi.org/10.54361/ajmas.258445

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