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

Sárka Hosková

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


Keywords

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

Full Text:

PDF

References

J. Beránek, J. Chvalina, Noncommutative Join Hypergroups of Affine Transformations of Ordered Fields, Dept.Math.Report Series 10, Univ.of South Bohemia, (2002), 15–22.

E. Cech, Topological Spaces, revised by Z. Frol´ık and M. Katˇetov, (Academia, Praha 1966).

P. Corsini, Prolegomena of Hypergroup Theory, (Aviani Editore Tricesimo 1993).

P. Corsini, V. Leoreanu, Applications of Hypergroup Theory, ( Kluwer Academic Publishers, Dordrecht, Hardbound, 2003).

J. Chvalina, Functional Graphs, Quasi-ordered Sets and Commutative Hypergroups, MU Brno (1995), (in Czech).

J. Chvalina, L. Chvalinová, Transposition hypergroups formed by transformation operators on rings of differentiable functions, Ital. J. Pure and Appl. Math., 13 pp. In print.

J. Chvalina, S. Hosková, Abelization of weakly associative hyperstructures based on their direct squares, Acta Mathematica et Informatica Universitatis Ostraviensis, Volume 11/2003, No. 1, 11–25.

J. Chvalina, S. Hosková, Join space of first-order linear partial differential operators with compatible proximity induced by a congruence on their group, Proc. of Mathematical and Computer modelling in Science and Engineering, Prague (2003), 166-170.

J. Chvalina, S. Hosková, Modelling of join spaces with proximities by first-order linear partial differential operators, submitted to Applications of Mathematics, 13p.

W.H. Gottschalk, G.A. Hedlund, Topological dynamics, AMS Colloq. Publ. Vol.XXXVI, Providence, Rhode Island, (1974) USA.

S. Hosková, Examples of abelization of hypergroups based on their direct products, Sborník VA, part B, 2, 7–19, (2002).

S. Hosková, Abelization of differential rings, Proc. of the 1st International mathematical workshop FAST VUT Brno, 2p., (2002).

S. Hosková, Abelization of a certain representation of non-commutative join space, Proc. of International Conference Aplimat 2003, Bratislava, Slovakia, (2003), 365–368.

S. Hosková, J. Chvalina, Abelization of proximal Hv-rings using graphs of good homomorphisms and diagonals of direct squares of hyperstructures, Proceedings of 8th Internat. Congress on AHA, Samothraki, Greece (2002), 147–159.

J. Jantosciak, Transposition in hypergroups, Algebraic Hyperstructures and Appl. Proc. Sixth Internat. Congress Prague 1996, Democritus Univ. of Thrace Press, Alexandroupolis (1997), 77–84.

J. Jantosciak, Transposition hypergroups: Noncommutative join spaces, J. Algebra 187 (1997), 97–119. http://dx.doi.org/10.1006/jabr.1997.6789

V. Leoreanu, On the hart of join spaces and of regular hypergroups, Riv. Mat. Pura Appl. No. 17 (1995), 133–142.

T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press Monographs in Mathematics, (Palm Harbor Florida 1994).

Abstract Views

1079
Metrics Loading ...

Metrics powered by PLOS ALM


 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Hypercompositional Algebra, Computer Science and Geometry
Gerasimos Massouros, Christos Massouros
Mathematics  vol: 8  issue: 8  first page: 1338  year: 2020  
doi: 10.3390/math8081338



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt