Exploring‎ ‎the ‎Algebraic‎ ‎Properties‎ ‎of Gyrosemigroups and a Characterization of Gyrosemigroups of Order 2

‎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...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics interdisciplinary research (Online) 2024-09, Vol.9 (3), p.255-267
Main Authors: Saeed Mirvakili, Raufeh Manaviyat, kazem Hamidizadeh
Format: Article
Language:English
Subjects:
groupoid
gyrogroup
gyrosemigroup
semigroup
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:‎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.
ISSN:2476-4965
DOI:10.22052/mir.2024.253354.1430