On clean hyperrings

Document Type : Research Paper

Authors

1 Department of Mathematics, Quchan Institute of Engineering and Technology , Quchan, Iran

2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Abstract

We introduce and study clean hyperrings. A hyperring R is called a clean hyperring if for every element x of R, x ∈ u + e where u is a unit and e is an idempotent. We also introduce GChyperring which is a proper generalization of clean hyperrings and obtain some related results of such hyperrings.

Keywords

References

[1] A. Asokkumar, , Derivations in Hyperrings and Prime Hyperrings, Iranian Jour-nal of Mathematical Sciences and Informatics, 8 (2013), 1-13.
[2] Irina Cristea, Sanja Jancic-Rasovic , Composition hyperrings, Analele Univ. Ovidius Constanta, 21 (2013), 81 94.
[3] P. Corsini, , Prolegomena of Hypergroup Theory. , Aviani Supplement to Riv. Mat. Pura Appl. 2nd ed. Editor, Tricesimo, (1993).
[4] P. Corsini, V. Leoreanu, , Applications of Hyperstructure Theory, Advances in Mathematics. Kluwer Academic Publishers, (2003).
[5] B. Davvaz, A. Salasi, A Realization of Hyperrings, Comm. Algebra,34 (2006),4389-4400.
[6] U. Dasgupta, On Prime and Primary Hyperideals of a Multiplicative Hyperring, Annals of the Alexandru Ioan Cuza University - Mathematics. Volume LVIII, Issue 1, Pages 19 36, ISSN (Print) 1221-8421, DOI: 10.2478/v10157-011-0039-7,
April 2012.
[7] M. Krasner, Approximation des Corps Values Complete de Characteristique p ΜΈ= 0 par ceux de Characteristique 0. Colloque d,Algebra superieure (Bruxelles, Decembre 1956), Bruxelles: C.B.R.M. (1957).
[8] M. Krasner, A Class of Hyperring and Hyperfields, Intern. J. Math. Sci. 6(1983),307-312.
[9] F. Marty, Sur une generalization de group, In:8i em Congres Math. Scandinaves:Stockholm, (1934),45-49.
[10] J. Mittas, Hypergroupes Canoniques, Mathematica Balkanica, 2 (1972),165-179.
[11] A. Nakassis, Recent Results in Hyperring and Hyperfield Theory, Intern. J. Math. Sci. 11 (1988),209-220.
[12] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc.229 (1977), 269-278.
[13] D. M. Olson, V. K. Ward, A Note on Multiplicative Hyperrings, Italian J. Pure Appl. Math. 1 (1997),77-84.
[14] R. Procesi, R. Rota, On some Classes of Hyperstructures, Discrete Math., 208/209 (1999),485-497.
[15] R. Rota, Sugli Iperanelli Moltiplicativi, Rend. di Mat. e delle sue Appl, Series VII, 4(1982),714-724.
[16] R. Rota, Hyperaffine Planes Over Hyperrings. Discrete Math.155 (1996),215-223.
[17] M. Stefanescu, Constructions of Hyperrings and Hyperfields. Advances in Abstract Algebra (ed. I. Tofan, M. Gontineac, M. Tarnauceanu) published by Alexandru Myller, Iasi, (2008), 4154.
[18] T. Vougiuklis, Hyperstructures and Their Representations, Palm Harber, USA, Hadronic Press, Inc. (1994).
[19] M. M Zahedi, R. Ameri, On the Prime, Primary and Maximal Subhypermodules, Italian Journal Pure and Applied Mathematics, 5 (1999),61-80. 
Journal of Hyperstructures
Volume 4, Issue 1
June 2015
Pages 1-10

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