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On quotient clean hyperring | ||
| Journal of Hyperstructures | ||
| دوره 4، شماره 2، اسفند 2015، صفحه 117-125 اصل مقاله (278.41 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2015.2602 | ||
| نویسنده | ||
| S. Ostadhadi-Dehkord* | ||
| Department of Mathematics, University of Hormozgan, P.O.Box 3995, Bandar Abbas, Iran | ||
| چکیده | ||
| In this paper, we introduce the notion of quotient Krasner hyperrings and prove that if I is a normal ideal of Krasner hyperring (R, +, ·), then quotient clean Krasner hyperring considered in [1] by Talebi et. al are just clean rings. | ||
| کلیدواژه‌ها | ||
| Krasner hyperring؛ Clean hyperring؛ Strong regular relation | ||
| مراجع | ||
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[1] T. Amouzegar and Y. Talebi, On clean hyperring, JHS, 4 (1) (2015), 1-10. [2] S. M. Anvariyeh and B. Davvaz, Strongly transitive geometric spaces associated to hypergroups, J. Algebra, 322 (2009), 1340 -1359. [3] S.M. Anvariyeh, S. Mirvakili and B. Davvaz, On Γ-hyperideals in Γ-semihypergroups, Carpathian J. Math., 26 (2010),11-23. [4] S.M. Anvariyeh, S. Mirvakili, B. Davvaz, θ∗- Relation on hypergroups and fundamental groups over commutative fundamental rings, Comm. Algebra, 36 (2) (2008), 622-631. [5] J. Zhan and I. Cristea, Γ-hypergroups: isomorphism and regular relations, U.P.B.Sci. Bull., Series A, 73 (4) (2011), 71-78. [6] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics vol.5 Kluwer Academic Publishers Dordrecht (2003). [7] P. Corsini, Prolegomena of hypergroup theory, Second Edition, Aviani Editore (1993). [8] B. Davvaz and V. Leoreanu-Fotea, Hyperring theory and applications, Interna-tional Academic Press USA (2007). [9] S. O. Dehkordi and B. Davvaz, A Strong Regular Relation on Γ-Semihyperrings.J. Sci. I.R. Iran., 22(3)(2011), 257-266. [10] S. O. Dehkordi, and B. Davvaz, Γ-semihyperrings: Approximations and rough ideals, Bull. Malays. Math. Sci. Soc., (2) 35(4) (2012), 1035-1047. [11] M. Krasner, A class of hyperrings and hyperfields, International J. Math. and Math. Sci., 6 (1983), 307-312. [12] F. Marty, Sur une generalization de la notion de group, 8th Congres Math. Scan-dinaves, (1934), 45-49. [13] C. G. Massouros, Free and cyclic hypergroups, Ann. Mat. Pure Appl., 150(5)(1998), 153-166. [14] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math.Soc., 229 (1977), 269-278. [15] W.K. Nicholson and Yiqiang Zhou, Clean rings: a survey. Advances in ring theory, World Scientific Publishing, Hackensack, NJ, (2005), 181–198. [16] J. Zhan, B. Davvaz and K. P. Shum, Isomorphism theorems of hypergroups, Acta Math. Sinica(Chinese Ser.), 50 (2007) 909-914. [17] Warren Wm. McGovern, Neat rings, Journal of Pure and Applied Algebra 205(2)(2006), 243–265. | ||
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