Penentuan Hiperstruktur Aljabar dan Karakteristiknya dalam Masalah Pewarisan Biologi

Abstract

This article discusses the application of mathematics in biological inheritance problems, which are closely linked to mathematical studies, particularly in algebraic hyperstructures, including hypergroupoids, hypergroups, and -semigroups. The research aims to determine types of algebraic hyperstructures arising from genetic crossing in inheritance issues, with the crossing results represented in a set where two distinct hyperoperations are applied. Findings indicate that under the first hyperoperation, the algebraic hyperstructures formed include a commutative hypergroup, a regular hypergroup, a cyclic hypergroup, and an -semigroup with one idempotent element, three identity elements, and one generator. Under the second hyperoperation the resulting algebraic hyperstructures include a commutative hypergroup, a regular hypergroup, a cyclic hypergroup, and an -semigroup without idempotent elements, with three identity elements and three generators. Future research could develop various alternative hyperoperations on biological inheritance problems, generating a greater variety of algebraic hyperstructures. The results of this study indicate that the algebraic hyperstructure of a set depends on its hyperoperation.

Keywords

• hyperstructure
• hypergroup
• semihypergroup
• n-hybrid
• inheritance