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The connection of hyper lattice implication algebras and related hyper algebras | ||
| Journal of Hyperstructures | ||
| دوره 5، شماره 2، اسفند 2016، صفحه 124-140 اصل مقاله (231.11 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2016.2674 | ||
| نویسنده | ||
| Shokoofeh Ghorbani* | ||
| Shahid Bahonar University of Kerman | ||
| چکیده | ||
| In this paper, we de ne the concepts of (good) con- gruences and strong congruences on hyper lattice implication alge- bras and use them to construct quotient hyper lattice implication algebras. We describe the relations between hyper lattice implica- tion algebra and hyper MV-algebra, hyper K-algebra, (weak) hyper residuated lattices. | ||
| کلیدواژه‌ها | ||
| (Quotient) Hyper lattice implication algebra؛ Congruence؛ Hyper MV-algebra؛ (weak) Hyper residuated lattice | ||
| مراجع | ||
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[1] R. A. Borzoei, A. Hasankhani and M. M. Zahedi, On hyper K-algebra, Math. Japonica, 52 (2000), 113-121. [2] R. A. Borzooei, M. Bakhshi and O. Zahiri, Filter theory on hyper residuated lattices Quasigroups and Related Systems, 22 (2014), 33 - 50. [3] R. A. Borzooei and S. Niazian, Weak hyper residuated lattices, Quasigroups and Related Systems, 21 (2013), 29 - 42. [4] P. Corsini and V. Leoreanu, Applications of hyperstructures theory, Adv in Math, Kluwer Acad Publ, 2003. [5] B. Davvaz, Polygroup theory and related systems. World Scientific, 2013. [6] S. Ghorbani, A. Hasankhani and E. Eslami, Hyper MV -algebras ,Set-Valued Mathematics and Aplications,1(2008)205-222. [7] S. Ghorbani, A. Hasankhani and E. Eslami, Quotient hyper MV-algebras, Sci. Math.e Japon., 3 (2007), 371-386. [8] S. Ghorbani, Hyper lattice implication algebras and some of their characteriza-tions, to appear. [9] F. Marty, Sur une generalization de la notion de groupe, in Proceedings of the 8th Congress des Mathematiciens Scandinaves, Stockholm, Sweden, (1934), 45 - 49. [10] J. Mittas, M. Konstantinidou, Sur une nouvelle generalisation de la notion de treillis. Les supertreillis et certaines de leurs proprietes generales, Ann. Sci. Univ. Blaise Pascal (Clermont II), Ser. Math. Fasc. 25 (1989), 61 - 83. [11] S. Rasouli and B. Davvaz, Lattices Derived from Hyperlattices, Commun. Alge-bra, 38 (2010), 2720-2737. | ||
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