Exploring the Algebraic Properties of Gyrosemigroups and a Characterization of Gyrosemigroups of Order 2
نویسندگان
1 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697,Tehran, I. R. Iran
2 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697,Tehran, I. R. Iran
3 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697,Tehran, I. R. Iran
doi
10.22052/mir.2024.253354.1430چکیده
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.
