Some properties of residual mapping and convexity in ∧-hyperlattices

Reza Ameri, Mohsen Amiri-Bideshki, A. Borumand Saeid

Abstract


The aime of this paper is the study of residual mappings and convexity in hyperlattices. To get this point, we study principal down set in hyperlattices and we give some conditions for a mapping between two hyperlattices to be equivalent with a residual maping. Also, we investigate convex subsets in ∧-hyperlattices.

Keywords


residuated map, convex, down-set, hyperideal, hy- perfilter

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References


R. Ameri, M. Amiri Bideshki and A. Borumand Saeid, On Prime Hyperfilter (hyperideal) in ∧-Hyperlattices, Submitted

R. Ameri and T. Nozari, ”A Connection Between Categories of Multialgebras and Algebra”, Italian Journal of Pure and Applied Mathematics, Vol. 27, 201-208, 2010.

R. Ameri and I.G. Rosenberg, ”Congruences of Multialgebras”, J. of Multi-Valued Logic & Soft Computing, Vol. 00, 1-12, 2009.

R. Ameri and M.M. Zahedi, ”Hyperalgebraic System”, Italian Journal of Pure and Applied Mathematics, Vol. 6, 21-39, 1999.

A. Asokkumar, ”Hyperlattice Formed by the Idempotents of a Hyperring”, International Journal of Mathematics, Vol. 38, 209-215, 2007.

B.B.N. Koguep, C. Nkuimi and C. Lele, ”On Fuzzy Ideals of Hyperlattice”, International Journal of Algebra, Vol. 2, 739-750. 2008.

M. Konstantinidou-Serafimidou, ”Modular Hyperlattices”, Γ Ranktika tes Akademias Athenon, Vol. 53, 202-218, 1978.

M. Konstantinidou-Serafimidou, ”Distributive and Complemented Hyperlattices”, PraKtika Tes Akademias Athenon, Vol. 56, 339-360, 1981.

M. Konstantinidou and J. Mittas, ”An introduction to the Theory of Hyperlattice”, Math. Balcanica, Vol. 7, 187- 193, 1977.

G.A. Moghani, A.R Ashrafi, ”On Some Hypergroups and Their Hyperlattice Structures”, Buletinul Academiei De Stiinte, Vol. 3, 15-24, 2003.

F. Marty, ”Surene generalization de la notion de group, In Eighth Congress Scandinaves”, Stockholm, 45-49, 1934.

G.E. Hansoul, ”A Simultianeous Characterization of Subalgebras and Conditional Sunalgebras of a Multialgebra”, Bull. Soc. Roy. Science Liego, Vol. 50, 16-19, 1981.

P. He, X. Xin and Jianming Zhan,”On Rough Hyperideals in Hyperlattices”, Journal of Applied and Mathematics, Vol. 2013, 10 Page.

H.E. Pickett, ”Subdirect Representations of Related System”, Fund. Math, Vol. 56, 223-240, 1964.

H.E. Pickett, ”Homomorphisms and Subalgebras of Multialgebras”, Pacific J. of Math, Vol. 21, 327-343, 1967.

C. Pelea, ”Multialgebras, Universal Algebra, and Identities”, J. Aust. Math, Vol. 81, 121-139, 2006.

C. Pelea,”On the Direct Limit of a Direct System of Multialgebras”,Direct Mathematics, Vol. 306, 2916-2930, 2006.

C. Pelea, ”Hyperring and α ∗ - Relations. A General Approach”, Journal of Algebra, Vol. 383, 104-128, 2013.

C. Pelea and I. Purdea, ”A Characterization Theorem For Complete Multialgebras”, Mathematica, 205-211, 2004.

A. Rahnemai-Barghi, ”The Prime Ideal Theorem for Distributive Hyperlattices”, Ital. J. Pure Appl. Math. , Vol. 10, 75-78, 2001.

S. Rasouli and B. Davvaz, ”Lattice Derived from Hyperlattices”, Communications in Algebra, Vol. 38, 2720- 2737, 2010.

S. Rasouli, B. Davvaz, ”Construction and Spectral Topology on Hyperlattice”, Mediterr. J. Math. , Vol. 7, 249- 262, 2010.

D. Schweigrt, ”Congruence Relation of multialgebra”, Discrete Mathematics”, Vol. 53, 249-253, 1985.

X.L. Xin and X.G. Li, ”On Hyperlattice and Quotient Hyperlattice”.




DOI: http://dx.doi.org/10.23755/rm.v27i1.30

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