Topological Krasner hyperrings with special emphasis on isomorphism theorems

Authors

DOI:

https://doi.org/10.4995/agt.2022.14778

Keywords:

topological hyperring, quotient hyperring, topological isomorphism

Abstract

Krasner hyperring is studied in topological flavor. It is seen that Krasner hyperring endowed with topology, when the topology is compatible with the hyperoperations in some sense, fruits new results comprising algebraic as well as topological properties such as topological isomorphism theorems.

Downloads

Download data is not yet available.

Author Biographies

Manooranjan Singha, University of North Bengal

Department of Mathematics

Kousik Das, University of North Bengal

Deparrtment of Mathematics

References

M. Al Tahan and B. Davvaz, Electrochemical cells as experimental verifications of n-ary hyperstructures, Matematika 35, no. 1 (2019), 13-24. https://doi.org/10.11113/matematika.v35.n1.1062

R. Ameri, M. Eyvazi and S. Hoskova-Mayerova, Superring of polynomials over a hyperring, Mathematics 7, no 10 (2019): 902. https://doi.org/10.3390/math7100902

R. Ameri, A. Kordi and S. Hoskova-Mayerova, Multiplicative hyperring of fractions and coprime hyperideals, An. Sţ. Univ. Ovidius Constanţa 25, no. 1 (2017), 5-23. https://doi.org/10.1515/auom-2017-0001

L. Berardi, F. Eugeni and S. Innamorati, Generalized designs, Linear spaces, Hypergroupoids and Algebraic Crypotography, IV Congress on AHA, Xanthi, 1990.

C. Berge, Graphes et Hypergraphes, Dunod, Paris, 1970.

H. Bordbar, I. Cristea and M. Novak, Height of hyperideals in Noetherian Krasner hyperrings, UPB Scientific Bulletin, Series A: Appl. Math. Phys. 79, no. 2 (2017), 31-42. https://doi.org/10.2298/FIL1719153B

B. Davvaz, Isomorphism theorems of hyperring, Indian J. Pure Appl. Math. 35, no. 3 (2004), 321-331.

B. Davvaz, A. Dehghan Nezhad and S. M. Moosavi Nejad, Algebraic hyperstructure of observable elementary particles including the Higgs boson, Proc. Nat. Acad. Sci. India Sect. A: Phys. Sci. 90, no. 1 (2020), 169-176. https://doi.org/10.1007/s40010-018-0553-z

B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, 115, Palm Harber, USA, 2007.

B. Davvaz and T. Musavi, Codes over hyperrings, Matematicki Vesnik 68, no. 1 (2016), 26-38.

D. Heidari, B. Davvaz and S. M. S. Modarres, Topological polygroups, Bull. Malays. Math. Sci. Soc. 39 (2016), 707-721. https://doi.org/10.1007/s40840-015-0136-y

D. Heidari, D. Mazaheri and B. Davvaz, Chemical salt reactions as algebraic hyperstructures, Iranian J. Math. Chem. 10, no. 2 (2019), 93-102.

S. Hoskova-Mayerova, Topological hypergroupoids, Comput. Math. Appl. 64, no. 9 (2012), 2845-2849. https://doi.org/10.1016/j.camwa.2012.04.017

A. Kehagias and M. Konstantinidou, Lattice ordered join space: an applications-oriented example, Italian J. Pure Appl. Math. (2000).

M. Konstantinidou, On the hyperlattices-ordered groupoids, Boll. Un. Mat. Ital. A (6) 2, no. 3 (1983), 343-350.

M. Krasner, A class of hyperrings and hyperfields, Int. J. Math. and Math. Sci. 6 (1983), 307-312. https://doi.org/10.1155/S0161171283000265

G. Ligozat, Weak representations of Interval Algebras, AAAI-90, Boston, 1990.

C. G. Massouros, On the theory of hyperrings and hyperfields, Algebra and Logic 24 (1985), 728-742. https://doi.org/10.1007/BF01978850

G. G. Massouros, Hypercompositional structures in the theory of the languages and automata, Analele Ştiinţifice ale Universităţii ''Al. I. Cuza", Iaşi, Tomul III, Informatica, 1994, 65-73.

A. Maturo, On a non-standard algebraic hyperstructure and its application to the coherent probability assessments, Italian J. Pure Appl. Math. 7 (2000), 33-50.

A. Mehrpooya, M. Ebrahimi and B. Davvaz, Two dissimilar approaches to dynamical systems on hyper MV-algebras and their information entropy, Eur. Phys. J. Plus 132 (2017): 379. https://doi.org/10.1140/epjp/i2017-11656-8

J. R. Munkres, Topology, 2nd Edition. Prentice Hall, 2000.

M. Norouzi and I. Cristea, Fundamental relation on m-idempotent hyperrings, Open Mathematics 15 (2017), 1558-1567. https://doi.org/10.1515/math-2017-0128

W. Phanthawimol, Y. Punkla, K. Kwakpatoon and Y. Kemprasit, On homomorphisms of Krasner hyperrings, An. Stiint. Univ. Al. I. Cuza Iasi. Mat.(S.N.) LVII (f.2) (2011), 239-246. https://doi.org/10.2478/v10157-011-0023-2

W. Prenowitz, Projective geometries as multigroups, Amer. J. Math. 65 (1943), 235-256. https://doi.org/10.2307/2371812

W. Prenowitz, Descriptive geometries as multigroups, Trans. Amer. Math. Soc. 59 (1946), 333-380. https://doi.org/10.1090/S0002-9947-1946-0015126-6

I. G. Rosenberg, Hypergroups induced by paths of a directed graph, Italian J. Pure Appl. Math. 4 (1998), 133-142.

M. S. Shadkami, M. R. Ahmadi Zand and B. Davvaz, The role of complete parts in topological polygroups, Int. J. Anal. Appl. 11 (2016), 54-60.

S. Spartalis, (H,R)-hyperring, Algebraic hyperstructutres and applications (Xanthi, 1990), World Sci. Publ., Teaneck, NJ, (1991), 187-195.

D. Stratigopoulos, Homomorphisms and Boolean hyperrings, Italian J. Pure Appl. Math. 17 (2005), 9-20.

G. Tallini, On Steiner hypergroups and Linear codes, Convegno Ipergruppi, Altre Strutture multivoche e loro applicazioni, Udine, 1985, 87-91.

V. Vahedi, M. Jafarpour, S. Hoskova-Mayerova, H. Aghabozorgi, V. Leoreanu-Fotea and S. Bekesiene, Derived hyperstructures from hyperconics, Mathematics 8, no. 3 (2020): 429. https://doi.org/10.3390/math8030429

S. Warner, Topological Rings, North-Holland, 1993.

Downloads

Published

2022-04-01

How to Cite

[1]
M. Singha and K. Das, “Topological Krasner hyperrings with special emphasis on isomorphism theorems”, Appl. Gen. Topol., vol. 23, no. 1, pp. 201–212, Apr. 2022.

Issue

Section

Articles