Abelization of join spaces of affine transformations of ordered field with proximity

Sárka Hosková


Using groups of affine transformations of linearly ordered fields a certain construction of non-commutative join hypergroups is presented based on the criterion of reproducibility of semi-hypergroups which are determined by ordered semigroups. The aim of this paper is to construct the abelization of the non-commutative join space of affine transformations of ordered fields. A construction of commutative weakly associative hypergroup (Hv-group) is made and a proximity is defined on this structure.


Transformation group; Join space; Abelization; Hyperoperation; Hyperstructures; Weak associativity

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doi: 10.3390/math8081338

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