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

• Main Author: Sárka Hosková
• Format: Article
• Language: English
• Published: Universitat Politècnica de València 2005-04-01
• Series: Applied General Topology
• Subjects: Transformation group; Join space; Abelization; Hyperoperation; Hyperstructures; Weak associativity
• Online Access: http://polipapers.upv.es/index.php/AGT/article/view/1963

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.