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A novel study on the structure of left almost hypermodules
Nabilah Abughazalah1, Shehzadi Salma Kanwal2, Mudsir Mehdi2
1Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
This study introduces the left almost hypermodule (LA-hypermodule), a new algebraic structure extending hypermodules. It explores its properties, variations from hypermodules, and connections to homomorphisms and relations.
Area of Science:
- Abstract Algebra
- Hypermodule Theory
Background:
- Introduces the novel concept of left almost hypermodules as an extension of hypermodules.
- Defines the left almost hypermodule (LA-hypermodule) as a structure acting on a left almost hyperring.
Purpose of the Study:
- To define and provide examples of the new LA-hypermodule structure.
- To explore the relationship between hypermodules and LA-hypermodules.
- To investigate the transition from left almost polygroups to LA-hypermodules.
Main Methods:
- Definition of left almost hypermodules.
- Examination of structural variations.
- Application of left almost polygroup concepts.
- Analysis of homomorphisms and regular relations.
Main Results:
- Provides a formal definition and examples of LA-hypermodules.
- Highlights key differences between hypermodules and LA-hypermodules.
- Establishes a framework for transitioning from left almost polygroups to LA-hypermodules.
- Observes outcomes related to homomorphisms and regular relations.
Conclusions:
- The LA-hypermodule is a significant new structure in abstract algebra.
- Further research into LA-hypermodules is warranted.
- The study lays the groundwork for exploring advanced properties and applications.
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