关于Γ-超半群上Green关系的若干研究
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摘要
考虑了文献[9]中提出的公开问题,并通过反例给出其否定的回答.在Γ-超半群中引入了弱吸收的概念,并通过举例阐述了弱吸收Γ-超半群未必是吸收的,进而解决了文献[9]中提出的另一个问题.作为Γ-超半群的推广,引入了(*,Γ)-超半群的概念,讨论了此类超半群上的Green关系.
A negative answer was given to the open problem on Green's relations of Γ-semihypergroups introduced in reference [9]. The concept of weakly absorbent Γ-semihypergroups was introduced, and a weakly absorbent Γ-semihypergroup is not necessarily absorbent was illustrated by an example. As an application of this result, the other problem investigated in the same paper as the above-mentioned was solved. The concept of(*,Γ)-semihypergroups was introduced and the Green's relations on this class of semihypergroups were studied in detail.
A negative answer was given to the open problem on Green's relations of Γ-semihypergroups introduced in reference [9]. The concept of weakly absorbent Γ-semihypergroups was introduced, and a weakly absorbent Γ-semihypergroup is not necessarily absorbent was illustrated by an example. As an application of this result, the other problem investigated in the same paper as the above-mentioned was solved. The concept of(*,Γ)-semihypergroups was introduced and the Green's relations on this class of semihypergroups were studied in detail.
引文
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[2]Amini M.Module Connes amenability of hypergroup measure algebras[J].Open Math,2015,13(1):737-756.
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[5]Corsini P,Shabir M,Mahmood T.Semisimple semihypergroups in terms of hyperideals and fuzzy hyperideals[J].Iranian Journal of Fuzzy Systems,2011,8(1):95-111.
[6]Hasankhani A.Ideals in a semihypergroup and Green's relations[J].Ratio Math,1999,13(13):29-36.
[7]Naka K,Hila K.Some properties of hyperideals in ternary semihypergroups[J].Math Slovaca,2013,63(3):449-468.
[8]Heidari D,Dehkordi O S,Davvaz B.Γ-semihypergroups and their properties[J].U P B Scientific Bulletin,Series A:Applied Mathematics and Physics,2010,72(1):195-208.
[9]Hila K,Davvaz B,Dine J.Study on the structure ofΓ-semihypergroups[J].Communications in Algebra,2012,40(8):2932-2948.
[10]Corsini P.Prolegomena of hypergroup theory[M].Tricesimo:Aviani Editore,1993.
[11]Hila K,Naka K.On pure hyperradical in semihypergroups[J].International Journal of Mathematics and Mathematical Sciences,2012,2012(2):876919.1-876919.7.
[12]Tang J,Dawaz B,Luo Y F.Hyperfilters and fuzzy hyperfilters of ordered semihypergroups[J].Journal of Intelligent&Fuzzy Systems,2015,29(1):75-84.
[13]Nordahl T E,Scheiblich H E.Regular*-semigroups[J].Semigroup Forum,1978,16(1):369-377.
[2]Amini M.Module Connes amenability of hypergroup measure algebras[J].Open Math,2015,13(1):737-756.
[3]Corsini P,Leoreanu-Fotea V.Applications of hyperstructure theory[M].Dordrecht:Adv Math,Kluwer Academic Publishers,2003.
[4]Corsini P.Sur les semihypergroupes[J].Atti Soc Pelorit Sci Fis Math Nat,1980,26(4):363-372.
[5]Corsini P,Shabir M,Mahmood T.Semisimple semihypergroups in terms of hyperideals and fuzzy hyperideals[J].Iranian Journal of Fuzzy Systems,2011,8(1):95-111.
[6]Hasankhani A.Ideals in a semihypergroup and Green's relations[J].Ratio Math,1999,13(13):29-36.
[7]Naka K,Hila K.Some properties of hyperideals in ternary semihypergroups[J].Math Slovaca,2013,63(3):449-468.
[8]Heidari D,Dehkordi O S,Davvaz B.Γ-semihypergroups and their properties[J].U P B Scientific Bulletin,Series A:Applied Mathematics and Physics,2010,72(1):195-208.
[9]Hila K,Davvaz B,Dine J.Study on the structure ofΓ-semihypergroups[J].Communications in Algebra,2012,40(8):2932-2948.
[10]Corsini P.Prolegomena of hypergroup theory[M].Tricesimo:Aviani Editore,1993.
[11]Hila K,Naka K.On pure hyperradical in semihypergroups[J].International Journal of Mathematics and Mathematical Sciences,2012,2012(2):876919.1-876919.7.
[12]Tang J,Dawaz B,Luo Y F.Hyperfilters and fuzzy hyperfilters of ordered semihypergroups[J].Journal of Intelligent&Fuzzy Systems,2015,29(1):75-84.
[13]Nordahl T E,Scheiblich H E.Regular*-semigroups[J].Semigroup Forum,1978,16(1):369-377.