A characterization for ε_m-complete hyperrings by m-complete parts

Subject Areas : Statistics

Morteza Norouzi ¹ (Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran)

Received: 2018-10-13 Accepted : 2020-11-22 Published : 2021-02-19

Keywords: رابطه ε_m, ابرحلقه, بخش کامل, رابطه منظم قوی,

Abstract :

In this paper, the concepts of m-complete parts in a hyperring are introduced and its connection with complete parts of a hyperring are investigated. Moreover, ε_m-complete hyperrings are defined based on ε_m-relation in hyperrings, and a characterization is obtained by m-complete parts for them.In this paper, the concepts of m-complete parts in a hyperring are introduced and its connection with complete parts of a hyperring are investigated. Moreover, ε_m-complete hyperrings are defined based on ε_m-relation in hyperrings, and a characterization is obtained by m-complete parts for them.In this paper, the concepts of m-complete parts in a hyperring are introduced and its connection with complete parts of a hyperring are investigated. Moreover, ε_m-complete hyperrings are defined based on ε_m-relation in hyperrings, and a characterization is obtained by m-complete parts for them.In this paper, the concepts of m-complete parts in a hyperring are introduced and its connection with complete parts of a hyperring are investigated. Moreover, ε_m-complete hyperrings are defined based on ε_m-relation in hyperrings, and a characterization is obtained by m-complete parts for them.

References:

[1]  F. Marty, (1934) Sur une generalization de la notion de groupe  congres des Mathematiciens Scandinaves, Stockholm, 45-49.

[2]  P. Corsini, (1993) Prolegomena of Hypergroup Theory, Second Eddition Aviani Editore.

 

[3]  P. Corsini, V. Leoreanu-Fotea, (2003) Applications of hyperstructure theory, Kluwer Academic Publishers, Dordrecht.

 

[4]  B. Davvaz, V. Leoreanu-Fotea, (2007) Hyperring Theory and Applications, International Academic Press, USA.

 

[5]  T. Vougiouklis, (1994) Hyperstructures and their representations, Hadronic Press Inc., Palm Harbor.

 

[6]  T. Vougiouklis, (1991) The fundamental relation in hyperrings. The general hyperfield, Algebraic hyperstructures and applications, Xanthi, World Sci. Publ., Teaneck, NJ., 203-211.

 

[7]  B. Davvaz, T. Vougiouklis, (2007) Commutative rings obtained from hyperrings ( -rings) with -relations, Communications in Algebra, 35 (11) 3307-3320.

 

[8]  R. Ameri, T. Nozari, (2010) A new characterization of fundamental relation on hyperrings, International Journal of Contemporary Mathematical Sciences, 5 (15) 721-738.

 

[9]  P. Ghiasvand, S. Mirvakili, B. Davvaz, (2017) Boolean rings obtained from hyperrings with -relation, Iranian Journal of Science and Technology, Transaction A: Science, 41 (1) 69-79.

 

[10]        S. Mirvakili, S.M. Anvariyeh, B. Davvaz, (2008) Transitivity of         -relation on hyperfields, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, 51 (3) 233-243.

 

[11]   M. Norouzi, I. Cristea, (2017) Fundamental relation on m-idempotent hyperrings, Open Mathematics, 15, 1558-1567.