### HYPERHROUPS AND Hv-GROUPS ASSOCIATED TO ELEMENTS WITH FOUR OXIDATION STATES

**DOI Number**

**First page**

**Last page**

#### Abstract

The theory of hyperstructures is of great importance due to its connections to various fields of Science. $H_v$-structures are hyperstructures where the equality is replaced by the nonempty intersection. This class of the hyperstructures is very large so one can use it in order to define several objects that they are not possible to be defined in the classical hyperstructure theory. This paper attempts an exposition of the connection between hyperstructure ($H_v$-structure) theory and certain type of chemical reactions. In this regard, we consider elements with four oxidation states and investigate their mathematical structures.

#### Keywords

#### Full Text:

PDF#### References

M. Al- Tahan, B. Davvaz, Weak chemical hyperstructures associated to electrochemical cells, Iranian Journal of Mathematical Chemistry, 9(1)(2018): 65-75.

M. Al- Tahan, B. Davvaz, Chemical hyperstructures for Astatine, Tellurium and for

Bismuth, Bull. Comput. Math., 7(1)(2019) 9–25.

M. Al- Tahan, B. Davvaz, Chemical hyperstructures for elements with four oxidation states, (submitted).

K.M. Chun, Chemical hyperstructures of chemical reactions for Titanium, Journal of the Chungcheong Mathematical Society, 30(4) (2017).

S.-C. Chung, K.M. Chun, N.J. Kim, S.Y. Jeong, H. Sim, J. Lee and H. Maeng, Chemical

hyperalgebras for three oxidation states of elements, MATCH Commun. Math. Comput. Chem., 72(2) (2014), 389-402.

P. Corsini, Prolegomena of Hypergroup Theory. Udine, Tricesimo, Italy: Second edition, Aviani editore, 1993.

P. Corsini and V. Leoreanu, Applications of Hyperstructures Theory, Advances in Mathematics, Kluwer Academic Publisher, 2003.

B. Davvaz, Polygroup Theory and Related Systems, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013. viii+200 pp.

B. Davvaz, Semihypergroup Theory, Elsevier/Academic Press, London, 2016. viii+156 pp.

B. Davvaz, Weak algebraic hyperstructures as a model for interpretation of chemical reactions, Iranian Journal of Mathematical Chemistry, 7(2) (2016) 267-283.

B. Davvaz and A. Dehgan Nezhad, Chemical examples in hypergroups, Ratio Matematica, 14 (2003), 71-74.

B. Davvaz, A brief survey of the theory of H v -structures, Proc. 8th International Congress on Algebraic Hyperstructures and Applications, 1-9 Sep., 2002, Samothraki, Hreece, Spanidis Press, (2003) 39-70.

B. Davvaz, A. Dehghan Nezhad and A. Benvidi, Chemical hyperalgebra: Dismutation reactions, MATCH Commun. Math. Comput. Chem., 67 (2012), 55-63.

B. Davvaz, A. Dehghan Nezhad and A. Benvidi, Chain reactions as experimental examples of ternary algebraic hyperstructures, MATCH Commun. Math. Comput. Chem.,

(2) (2011), 491-499.

B. Davvaz, A. Dehghan Nezhad and M. Mazloum-Ardakani, Chemical hyperalgebra: Redox reactions, MATCH Commun. Math. Comput. Chem., 71 (2014), 323-331.

B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007.

B. Douglas, D. H. McDaniel, and J. J. Alexander, Concepts and Models of Inorganic Chemistry, 2nd ed. John Wiely & Sons, Inc. 1985.

F. Marty, Sur une generalization de la notion de group, In: 8th Congress Math. Scandenaves, (1934), pp. 45-49.

T. Vougiouklis, H v -groups defined on the same set, Discrete Math., 155 (1996) 259-265.

T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Inc, 115, Palm Harber, USA, 1994.

T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, In: Proc. Fourth Int. Congress on Algebraic Hyperstructures and Appl. (AHA 1990),

World Scientific, 1991, pp. 203-211.

DOI: https://doi.org/10.22190/FUMI1904689A

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)