Distributive and Dual Distributive Elements in Hyperlattices

Ameri, Reza; Amiri-Bideshki, M.; Hoskova-Mayerova, Sarka; Saeid, A. B.

doi:10.1515/auom-2017-0032

Abstract

In this paper we introduce and study distributive elements, dual distributive elements in hyperlattices, and prove that these elements forms ∧-semi lattice and ∨-semi hyperlattice, respectively. We use the properties of prime ideals and prime filters in hyperlattices. We will proceed to introduce the notion of dual distributive hyperlattices, I-filters and filters generated by dual distributive elements. Finally, the relationship between good homomorphisms and istributive (resp. dual distributive)elements in hyperlattices are investigated.

References

[1] H. AGHABOZORGHI, I.CRISTEA, M. JAFARPOUR, On comple- mentable semihypergroups, Comm. Algebra, 44(4) (2016), 1740-1753.10.1080/00927872.2015.1027395
Search in Google Scholar Back to article
[2] R. AMERI, M. AMIRI-BIDESHKI, A. B. SAEID and S. HOSKOVA- MAYEROVA, Prime filters of hyperlatices, An. Stiint. Univ. \Ovidius" Constanta Ser. Mat., 24(2), (2016), 15-26.10.1515/auom-2016-0025
Search in Google Scholar Back to article
[3] G. BIRKHOFF, Lattice Theory, American Mathematical Society Collogu- ium Publications [M], Providence, Rhode Island, 1940.
Search in Google Scholar Back to article
[4] J. CHVALINA, S. HOSKOVA-MAYEROVA, A. DEGHAN NEZHAD, General actions of hypergroups and some applications, An. Stiint. Univ. \Ovidius" Constanta Ser. Mat., 21(1), (2013), 59-82.10.2478/auom-2013-0004
Search in Google Scholar Back to article
[5] J. CHVALINA, S. HOSKOVA-MAYEROVA, On certain proximities and preorderings on the transposition hypergroups of linear first-order partial difierential operators, An. Stiint. Univ. \Ovidius" Constanta Ser. Mat., 22(1), (2014), 85-103.10.2478/auom-2014-0008
Search in Google Scholar Back to article
[6] P. CORSINI, V. LEOREANU, Applications of Hyperstructure Theory, Kluwer Academic Publishers, Dordrecht, Hardbound, 2003.10.1007/978-1-4757-3714-1
Search in Google Scholar Back to article
[7] I. CRISTEA, S. JANCIC-RASOVIC, Compositions Hyperrings, An. Sti- int. Univ. \Ovidius" Constanta Ser. Mat., 21(2), (2013), 81-94.10.2478/auom-2013-0024
Search in Google Scholar Back to article
[8] I. CRISTEA, Regularity of Intuitionistic Fuzzy Relations on Hyper- groupoids, An. Stiint. Univ. \Ovidius" Constanta Ser. Mat., 22(1), (2014), 105-119.10.2478/auom-2014-0009
Search in Google Scholar Back to article
[9] I. CRISTEA, S. HOSKOVA, Fuzzy pseudotopological hypergroupoids, Iran. J. Fuzzy Syst., 6(4), (2009), 11-19.
Search in Google Scholar Back to article
[10] K. HASILOVfiA, Iterative Method for Bandwidth Selection in Kernel Discriminant Analysis.In: 32nd International Conference Mathematical Methods in Economics MME2014. Olomouc: Palackfiy University, Olomouc, (2014), 263-268.
Search in Google Scholar Back to article
[11] S. HOSKOVA, Topological hypergroupoids, Comput. Math. Appl., 64(9)(2012), 2845-2849.10.1016/j.camwa.2012.04.017
Open DOI Search in Google Scholar Back to article
[12] B. B. N. KOGUEP, C. NKUIMI, C. LELE, On fuzzy ideals of hyperlattice, Internat. J. Algebra, 2(2008), 739-750.
Search in Google Scholar Back to article
[13] M. KONSTANTINIDOU, J. MITTAS, An introduction to the theory of hyperlattice, Math. Balcanica, 7(1977), 187-193.
Search in Google Scholar Back to article
[14] M. KRASNER, A class of hyperrings and hyperfields, Int. J. Math. and Math. Sci., 2(1983), 307-312.10.1155/S0161171283000265
Open DOI Search in Google Scholar Back to article
[15] F. MARTY, Surene generalization de la notion de group, Eighth Congress Scandinaves, Stockholm, (1934), 45-49.
Search in Google Scholar Back to article
[16] M. NOROUZI, I. CRISTEA, A note on composition (m,n)-hyperrings, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat., 25(2) (2017)10.1515/auom-2017-0023
Search in Google Scholar Back to article
[17] M.fiC. MIKUfiSKOVfiA, M. SEDLAfiCfiIK, The application of regression trees to modelling ozone concentration measured in selected regions, Mendel 2016, 241-248.
Search in Google Scholar Back to article
[18] M. NOVfiAK, Some basic properties of EL-hyperstructures, European J. of Combin. 34(2013), 446-459.10.1016/j.ejc.2012.09.005
Search in Google Scholar Back to article
[19] M. NOVfiAK, n-ary hyperstructures constructed from binary quasi-orderer semigroups, An. Stiint. Univ. \Ovidius" Constanta Ser. Mat., 22(3), (2014), 147-168.10.2478/auom-2014-0056
Search in Google Scholar Back to article
[20] A. RAHNEMAI-BARGHI, The prime ideal theorem for distributive hy- perlattices, Ital. J. Pure Appl. Math., 10(2010), 75-78.
Search in Google Scholar Back to article
[21] S. RASOULI, B. DAVVAZ, Lattice derived from hyperlattices, Comm. in Algebra, 38(2010), 2720-2737.10.1080/00927870903055230
Search in Google Scholar Back to article
[22] S. RASOULI, B. DAVVAZ, Construction and spectral topology on hy- perlattice, Mediterr. J. Math., 7(2010), 249-262.10.1007/s00009-010-0065-9
Search in Google Scholar Back to article
[23] T. VOUGIOUKLIS, Hyperstructures and their Representations, Hadronic Press, Inc., 1994.
Search in Google Scholar Back to article

Distributive and Dual Distributive Elements in Hyperlattices

Abstract

Paradigm

My account