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

Document Type : Original Scientific Paper

Authors

‎Department of Mathematics, Payame Noor University‎, ‎P.O.Box 19395-3697,Tehran‎, ‎I‎. ‎R‎. ‎Iran

10.22052/mir.2024.253354.1430

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.

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References

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Mathematics Interdisciplinary Research
Volume 9, Issue 3
In progress
September 2024
Pages 255-267

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