BİR HİPERGRUBUN ALTHİPERGRUPLARININ KAFESİ

Yıl 2019, Cilt: 7 Sayı: 2, 159 - 165, 23.08.2019

Dilek Bayrak

https://doi.org/10.20290/estubtdb.507321

Öz

Tarnauceanu [On the poset of
subhypergroups of a hypergroup, Int. J. Open Problems Comp. Math. 3(2) (2010)
505-508] çalışmasında bir hipergrubun althipergruplarının kısmen sıralı kümesi
hakkında bazı açık problemler verdi. Biz bu çalışmada, bir hipergrubun althipergruplarının
bazı özel altposetllerinin modüler veya dağılmalı kafes olduğu elde ettik.

Anahtar Kelimeler

hipergrup, althipergrup, kafes, dağılmalı kafes

THE LATTICE OF SUBHYPERGROUPS OF A HYPERGROUP

Öz

Tarnauceanu [On the poset of
subhypergroups of a hypergroup, Int. J. Open Problems Comp. Math. 3(2) (2010)
505-508] gave some open problems concerning to the set of subhypergroups of a
hypergroup, partially ordered by set inclusion. In this study, we obtain that
some certain subposets of subhypergroups of a hypergroup are modular or
distributive lattice.

Anahtar Kelimeler

hypergroup, subhypergroup, lattice, distributive lattice

Kaynakça

• [1] Birhoff, G., Lattice Theory, Amer. Math. Soc. Colloq. Publ., 1967.
• [2] Corsini, P. and Leoreanu V., Application of Hyperstructure Theory, Kluwer Academic Publishers, 2003.
• [3] Davvaz, B. and Leoreanu ,V., Hyperring theory and applications, International Academic Press, 2007.
• [4] Marty, F, Sur ungeneralisation de la notion degroup, 8th Congress of Scandinavian Mathematicians, 45-49, 1934.
• [5] Tarnauceanu, M. On the poset of subhypergroups of a hypergroup, Int. J. Open Problems Comp. Math. 3(2), 115-122, 2010.
• [6] Massouros, C.G., Some properties of certain subhypergroups, Ratio Mathematica, 25, 67-76, 2013.
• [7] Schmidt, R., Subgroup Lattices of Groups, de Gruyter Expositions in Mathematics 14, de Gruyter, Berlin, 1994.