دانشگاه گیلان
معاونت پژوهش و فناوری دانشگاه گیلان
انتشارات دانشگاه گیلان

 آمار

تعداد نشریات31
تعداد شماره‌ها766
تعداد مقالات7,260
تعداد مشاهده مقاله10,623,601
تعداد دریافت فایل اصل مقاله7,093,732
Mirvakili, S., Ghazavi, S. H., Dehghanizadeh, M. A.. (1402). On enumeration and classification of $EL^2$-semihypergroups and $EL^2$-$H_v$-semihypergroups with 2 elements. فیزیولوژی و بیوتکنولوژی آبزیان, 11(2), 85-97. doi: 10.22124/jart.2023.23376.1468
S. Mirvakili; S. H. Ghazavi; M. A. Dehghanizadeh. "On enumeration and classification of $EL^2$-semihypergroups and $EL^2$-$H_v$-semihypergroups with 2 elements". فیزیولوژی و بیوتکنولوژی آبزیان, 11, 2, 1402, 85-97. doi: 10.22124/jart.2023.23376.1468
Mirvakili, S., Ghazavi, S. H., Dehghanizadeh, M. A.. (1402). 'On enumeration and classification of $EL^2$-semihypergroups and $EL^2$-$H_v$-semihypergroups with 2 elements', فیزیولوژی و بیوتکنولوژی آبزیان, 11(2), pp. 85-97. doi: 10.22124/jart.2023.23376.1468
Mirvakili, S., Ghazavi, S. H., Dehghanizadeh, M. A.. On enumeration and classification of $EL^2$-semihypergroups and $EL^2$-$H_v$-semihypergroups with 2 elements. فیزیولوژی و بیوتکنولوژی آبزیان, 1402; 11(2): 85-97. doi: 10.22124/jart.2023.23376.1468

On enumeration and classification of $EL^2$-semihypergroups and $EL^2$-$H_v$-semihypergroups with 2 elements

Journal of Algebra and Related Topics
دوره 11، شماره 2، اسفند 2023، صفحه 85-97    اصل مقاله (111.06 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2023.23376.1468
نویسندگان
S. Mirvakili* 1؛ S. H. Ghazavi2؛ M. A. Dehghanizadeh3
1Department of Mathematics, Payame Noor University, P.O.BOX 19395-3697 Tehran, Iran,
2Department of Mathematics, Shahid Ashrafi Esfahani University, Isfahan, Iran
3Technical and Vocational University(TVU), Tehran, Iran
چکیده
$EL$-hypergroups were defined by Chvalina 1995. Till
now, no exact statistics of $EL$-hypergroups have been done.\\ Moreover, there is no classification of $EL$-hypergroups and $EL^2$-hypergroups even over small sets.
In this paper, we classify all $EL$-(semi)hypergroups over sets with
two elements obtained from quasi ordered semigroups. Also, we characterize all quasi ordered $H_v$-group and then we enumerate the number of $EL^2$-$H_v$-hypergroups and $EL^2$-hypergroups of order 2.
کلیدواژه‌ها
Ends lemma؛ $EL$-hypergroups؛ $H_v$-group؛ quasi order relation؛ partially order relation
مراجع
1. R. Bayon, N. Lygeros, Advanced results in enumeration of hyperstructures, J. Algebra, (2)320 (2008), 821-835,
2. J. Chvalina, Functional Graphs, Quasi-Ordered Sets and Commutative Hyper-
groups, Masaryk University, Brno, (1995), (in Czech).
3. P. Corsini, Prolegomena of Hypergroup Theory, Aviani, Udine, 2003.
4. P. Corsini, V. Leoreanu-Fotea, Applications of Hyperstruture Theory, Kluwer
Academic Publishers, 2003.
5. B. Davvaz, Semihypergroup Theory, Elsevier, 2016.
6. B. Davvaz, Polygroup Theory and Related System, World Scienti c Publishing
Co. Pte. Ltd., 2012.
7. B. Davvaz and T. Vougiouklis, A Walk Through Weak Hyperstructures; Hv-
Structure, World Scienti c Publishing Co. Pte. Ltd., Hackensack, NJ, 2019.
8. A. Distler, Classi cation and Enumeration of Finite Semigroups, Ph.D. Thesis, University of St Andrews, (2010).
9. S. H. Ghazavi and S. Mirvakili, On enumeration of EL{hyperstructures with 2
elements, J. Mahani Math. Res. Cent., (1) 11 (2022), 145-158.
10. S. H. Ghazavi, S. M. Anvarieh and S. Mirvakili, EL2{hyperstructures derived
from (partially) quasi ordered hyperstructures, Iran. J. Math. Sci. Inform. (2)
10 (2015), 99-114.
11. S. H. Ghazavi, S. M. Anvarieh and S. Mirvakili, Ideals in EL-semihypergroups
associated to ordered semigroups, J. Algebr. Syst. (2) 3 (2016), 109-125.
12. S. H. Ghazavi and S. M. Anvarieh, EL-hyperstructures associated to n-ary
relations, Soft Computing, 21 (2013), 5841-5850.
13. S. Hoskova, Binary hyperstructures determined by relational and transformation
systems, Habilitation Thesis, Faculty of Science, Universityof Ostrava, 2008.
14. R. Migliorato, Ipergruppi di cardinalit 3 e isomor smi di ipergruppoidi commu-
tativi totalmente regolari, Atti Convegno su Ipergruppi, Udine, 1985.
15. G. Nordo, An algorithm on number of isomorphism classes of hypergroups of
order 3, Italian J. Pure Appl. Math. 2(1997), 37-42.
16. M. Novak, Potential of the Ends lemma to create ring-like hyperstructures from
quasi-ordered (semi)groups, South Bohemia Mathem. Letters, (1) 17 (2009), 39-50.
17. M. Novak, The notion of subhyperstructure of "Ends lemma"-based hyperstructures, Journal of Applied Mathematics, 3 (2) (2010), 237-247.

18. M. Novak, Important elements of EL-hyperstructures, in APLIMAT:10th In-
ternational Conference, STU in Bratislava, Bratislava, (2011), 151-158.
19. M. Novak, El-hyperstructures: an overview, Ratio Mathematica, 23 (2012), 65-80.
20. M. Novak, Some basic properties of EL-hyperstructure, European J. Combin. 34 (2013), 446-459.
21. M. Novak, On EL-semihypergroup, European J. Combin. 44 (2015), 274-286.
22. P. Rackova, Hypergroups of symmetric matrices, 10th International Congress
of Algebraic Hyperstructures and Applications, Proceeding of AHA, (2008).
23. I. G. Rosenberg, Hypergroups and join spaces determined by relations, Italian
Journal of Pure and Applied Mathematics, 4 (1998), 93-101.
24. Ch. Tsitouras and Ch. G. Massouros, On enumeration of hypergroups of order
3, Comput. Math. Appl. 59 (2010) 519-523.
25. T. Vougiouklis, The e-hyperstructures, J. Mahani Math. Res. Cent. 1(1)(2012)13-28.
26. T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Florida, 1994.

آمار
تعداد مشاهده مقاله: 113
تعداد دریافت فایل اصل مقاله: 197


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب