Exploring the Algebraic Properties of Gyrosemigroups and a Characterization of Gyrosemigroups of Order 2
Year: 2024
Type: article
Abstract: A significant development in the field of gyrogroups was the introduction of the space of all relativistically admissible velocities, which brought gyrogroups into the mainstream. A group has various generalizations, one of which is the notion of gyrogroups. Moreover, for any pair (a, b) in this structure, there exists an automorphism gyr[a, b] that fulfills left associativity and left loop property. The motivation behind this study is to generalize gyrogroups and semigroups, which has led to the introduction of gyrosemigroups. Accordingly, in this paper, some classes of gyrosemigroups are presented. Also, all gyrosemigroups of order 2 are characterized. Furthermore, the gyrosemigroups with an identity or a zero are studied.
Institution: Payame Noor University
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6945226603
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