On Regular Γ-semihyperrings and Idempotent Γ-semihyperrings
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The Γ-semihyperring is a generalization of the concepts of a semiring, a semihyperring and a Γ-semiring. Here, the notions of (strongly) regular Γ-semihyperring, idempotent Γ-emihyperring; invertible set, invertible element in a Γ-semihyperring are introduced, and several examples given. It is proved that if all subsets of Γ-semihyperring are strongly regular then for every Δ⊆ Γ, there is a Δ-idempotent subset of R. Regularity conditions of Γ-semihyperrings in terms of ideals of Γ-semihyperrings are also characterized.
Abstract
The Γ-semihyperring is a generalization of the concepts of a semiring, a semihyperring and a Γ-semiring. Here, the notions of (strongly) regular Γ-semihyperring, idempotent Γ-emihyperring; invertible set, invertible element in a Γ-semihyperring are introduced, and several examples given. It is proved that if all subsets of Γ-semihyperring are strongly regular then for every Δ⊆ Γ, there is a Δ-idempotent subset of R. Regularity conditions of Γ-semihyperrings in terms of ideals of Γ-semihyperrings are also characterized.
참고문헌 (18)
- R. Ameri, "On k-hyperideals of semihyperrings", J. Discrete Math. Sci. Cryptogr, 10(1), pp.41~54 (2007)
- S. M. Anvariyeh, "On Γ-hyperideals in Γ-semihypergroups", Carpathian J. Math, 26, pp.11~23 (2010)
- W. E. Barenes, "On the Γ-rings of Nobusawa", Pacific J. Math, 18, pp.411~422 (1966)
- P. Corsini, "Prolegomena of hypergroup theory" (1993), Aviani Editore
- P. Corsini, "Applications of hyperstructure theory" (2003), Kluwr Academic Publishers
- B. Davvaz, "Hyperring theory and applications" (2007), International Academic Press
- S. O. Dehkordi, "A strong regular relation on Γ-semihyperrings", J. Sci. Islam. Repub. Iran, 22(3), pp.257~266 (2011)
- S. O. Dehkordi, "Γ-semihyperrings : Approximations and rough ideals", Bull. Malays. Math. Soc, 35(4), pp.1035~1047 (2012)
- S. O. Dehkordi, "Γ-semihyperring : Fundamental rings and complex product", Bull. Allahabad Math. Soc, 29(2), pp.111~135 (2014)
- S. O. Dehkordi, "Γ-semihyperrings: ideals, homomorphisms and regular relations", Afr. Mat, 26, pp.849~861 (2015)
- H. Hedayati, "Fundamental relation on Γ-hyperrings", Ars Combin, 100, pp.381~394 (2011)
- D. Heidari, "Γ-semihypergroups and their properties", Politehn. Univ. Bucharest Sci. Bull. Ser. A : Appl. Math. Phys, 72, pp.195~208 (2010)
- S. Krishnamoorthy, "Commuting regular Γ-semiring", Int. J. Math. Comput. Sci, 4(8), pp.376~378 (2010)
- F. Marty, "Sur une generalization de la notion de groupe", 8th congres des Mathematicians Scandinaves, pp.45~49 (1934)
- N. Nobusawa, "On generalization of the ring theory", Osaka J. Math, 1(1), pp.81~89 (1964)
- S. Ostadhadi-Dehkordi, "Ideal theory in Γ-semihyperrings", Iran. J. Sci. Tech. Trans. A Sci, 37(3), pp.251~263 (2013)
- M. M. K. Rao, "Γ-semirings. I", Southeast Asian Bull. Math, 19(1), pp.49~54 (1995)
- T. Vougiouklis, "On some representations of hypergroups", Ann. Sci. Univ. Clermont-Ferrand II : Math, 26, pp.21~29 (1990)