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...

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Published in:Mathematics interdisciplinary research (Online) 2024-09, Vol.9 (3), p.255-267
Main Authors: Saeed Mirvakili, Raufeh Manaviyat, kazem Hamidizadeh
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groupoid
gyrogroup
gyrosemigroup
semigroup
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Raufeh Manaviyat
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description ‎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.
doi_str_mv 10.22052/mir.2024.253354.1430
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subjects groupoid
gyrogroup
gyrosemigroup
semigroup
title Exploring‎ ‎the ‎Algebraic‎ ‎Properties‎ ‎of Gyrosemigroups and a Characterization of Gyrosemigroups of Order 2
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