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

Sárka Hosková

doi:10.4995/agt.2005.1963

Authors

Sárka Hosková University of Defence Brno

DOI:

https://doi.org/10.4995/agt.2005.1963

Keywords:

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

Abstract

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 (H_v-group) is made and a proximity is defined on this structure.

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Author Biography

Sárka Hosková, University of Defence Brno

Department of Mathematic

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