Hv-module of functions over Hv-ring of arithmetics and it’s fundamental module

Al Tahan, M.; Davvaz, B.

doi:10.2478/auom-2024-0001

Abstract

After introducing the definition of hypergroups by Marty, the study of hyperstructures and its connections with other fields has been of great importance. In this paper, we continue the investigation between hyperstructure theory and number theory. More precisely, we define an H_v-module of complex valued functions over the H_v-ring of arithmetics, classify its complete parts, the strongly regular relations on it and identify its fundamental module.

References

M. Al-Tahan and B. Davvaz, On the existence of hyperrings associated to arithmetic functions, J. Number Theory, 174 (2017), 136–149.
Search in Google Scholar Back to article
M. Al-Tahan and and B. Davvaz, Strongly regular relations of arithmetic functions, J. Number Theory, 187 (2018), 391–402.
Search in Google Scholar Back to article
M. Asghari-Larimi and B. Davvaz, Hyperstructures associated to arithmetic functions, Ars Combin., 97 (2010), 51–63.
Search in Google Scholar Back to article
P. Corsini, Prolegomena of Hypergroup Theory, Udine, Tricesimo, Italy: Second edition, Aviani editore, 1993.
Search in Google Scholar Back to article
P. Corsini, Contributo alla teoria degli ipergruppi, Atti Soc. Pelor. Sc. Mat. Fis. Nat. Messina, Messina, Italy, (1980), 1–22.
Search in Google Scholar Back to article
P. Corsini and and V. Leoreanu, Applications of Hyperstructures Theory, Advances in Mathematics, Kluwer Academic Publisher, 2003.
Search in Google Scholar Back to article
B. Davvaz, Polygroup Theory and Related Systems, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013, viii+200 pp.
Search in Google Scholar Back to article
B. Davvaz, Semihypergroup Theory, Elsevier/Academic Press, London, 2016, viii+156 pp.
Search in Google Scholar Back to article
B. Davvaz and and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007.
Search in Google Scholar Back to article
B. Davvaz and T. Vougiouklis, A walk through weak hyperstructures: H_v-structures, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2019, xi+334 pp.
Search in Google Scholar Back to article
D. Freni, A note on the core of a hypergroup and the transitive closure β* of β, Riv. Mat. Pura Appl., 8 (1991), 153–156.
Search in Google Scholar Back to article
M. Koskas, Groupoides, demi-hypergroupes et hypergroupes, J. Math. Pure Appl., (9) 49 (1970), 155–192.
Search in Google Scholar Back to article
F. Marty, Sur une generalization de la notion de group, In 8th Congress Math. Scandenaves, (1934), pp. 45–49.
Search in Google Scholar Back to article
Y. Sureau, Contribution a la thorie des hypergroupes et hypergroupes opérant transivement sur un ensemble, Doctoral Thesis, (1980).
Search in Google Scholar Back to article
T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Inc, 115, Palm Harber, USA, 1994.
Search in Google Scholar Back to article
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, 203–211.
Search in Google Scholar Back to article

Hv-module of functions over Hv-ring of arithmetics and it’s fundamental module

Abstract

Paradigm

My account