Algorithms for Finding Specific Elements in Algebraic‎ ‎Hyperstructures‎ ‎with‎ ‎One Hyperoperation

Document Type : Original Scientific Paper

Authors

‎Department of Mathematical Sciences, ‎Yazd University,‎Yazd‎, ‎I‎. ‎R‎. ‎Iran

Abstract

‎In this paper‎, ‎first‎, ‎we show how to define an algebraic hyperstructure by using algorithms‎. ‎Then‎, ‎we present algorithms that calculate specific elements in algebraic hyperstructures‎. ‎These specific elements are‎: ‎scalars‎, ‎scalar identities‎, ‎identities‎, ‎inverses‎, ‎zero elements‎, ‎right simplifiable elements‎, ‎left simplifiable elements‎, ‎left absorbing-like elements and right absorbing-like elements‎. ‎We also introduce some algorithms in algebraic hyperstructures to check properties or calculate specific members‎. ‎These algorithms are presented for algebraic hyperstructures with one hyperoperation‎, ‎i.e‎. ‎hypergroupoids‎. ‎However‎, ‎they can be developed for other algebraic hyperstructures‎.

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References

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Mathematics Interdisciplinary Research
Volume 10, Issue 1
March 2025
Pages 49-70

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