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http://dx.doi.org/10.11568/kjm.2021.29.2.305

ON L-FUZZY SEMI-PRIME IDEALS OF A POSET AND SEPARATION THEOREMS  

Engidaw, Derso Abeje (Department of Mathematics, University of Gondar)
Alemu, Tilahun Bimerew (Department of Mathematics, University of Gondar)
Publication Information
Korean Journal of Mathematics / v.29, no.2, 2021 , pp. 305-320 More about this Journal
Abstract
In this paper, the relations between L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of a poset and L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of the lattice of all ideals of a poset are established. A result analogous to Separation Theorem is obtained using L-fuzzy semi-prime ideals.
Keywords
Poset; Prime Ideal; Semiprime Ideal; L-Fuzzy prime Ideal; L-fuzzy Semi-prime Ideal;
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1 U. Acar, On L-fuzzy prime submodules, Hacet. J. Math. Stat., 34 (2005) 17-25.
2 B. A. Alaba and G. M. Addis, L-Fuzzy ideals in universal algebras, Ann. Fuzzy Math. Inform., 17(1), (2019) 31-39.   DOI
3 A. K. Katsaras and D.B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J. Math. Anal. Appl. 58 (1977) 135-146.   DOI
4 Davey, B. A., Priestley, H. A., Introduction to Lattices and Order , Cambridge University Press, 1990.
5 R. Halas, Annihilators and ideals in ordered sets , Czechoslovak Math. J. 45(120) (1995), 127-134.   DOI
6 G.Gratzer, General Lattice Theory , Academic Press, New York, 1978.
7 N. Ajmal and K. V. Thomas, Fuzzy lattices, Inform. Sci, 79 (1994) 271-291.   DOI
8 B. A. Alaba and G. M. Addis, L-Fuzzy semi-prime ideals in universal algebras, Korean J. Math., 27(2), (2019), 327-340.
9 B. A. Alaba, M. A. Taye and D. A. Engidaw, L-Fuzzy ideals of a poset, Ann. Fuzzy Math. Inform. 16 (2018), 285-299.   DOI
10 R. Ameri and R. Mahjoob, The spectrum of prime L- submodules, Fuzzy Sets and Systems 159, (2008) 1107-1115.   DOI
11 J. A. Goguen, L-fuzzy sets , J. Math. Anal. Appl. 18 (1967) 145-174.   DOI
12 B. B. Makamba, and V. Murali, On prime fuzzy submodules and radicals, J. Fuzzy Math. 8(4) (2000) 831-843.
13 Y. Rav, Semiprime ideals in general lattices , J. Pure Appl. Algebra, 56 (1989) 105-118.   DOI
14 B. A. Alaba and D. A. Engidaw, L-Fuzzy semiprime ideals of a poset, Advances in Fuzzy Systems, Vol. 2020, Article ID 1834970, 10 pages, 2020.
15 Kumar, R., Fuzzy ideals and fuzzy semiprime ideals, Inform. Sci. 66 (1992) 43-52.   DOI
16 V. S. Kharat and K. A. Mokbel, Semi-prime ideals and separation theorem in posets, Order, 25(3) (2008), 195 - 210.   DOI
17 V. S. Kharat and K. A. Mokbel, Primeness and semiprimeness in posets , Math. Bohem. 134(1) (2009), 19-30.   DOI
18 B. B. N. Koguep and C. Lele, On fuzzy prime ideals of lattices, SJPAM 3(2008) 1-11.
19 H.V. Kumbhojkar and M.S. Bapat, On semiprime fuzzy ideals, Fuzzy Sets and Systems 60 (1993) 219-223.   DOI
20 A. Rosenfeld, Fuzzy groups , J. Math. Anal. Appl. 35 (1971) 512-517.   DOI
21 M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936) 37-111.   DOI
22 U. M. Swamy and D. V. Raju, Fuzzy Ideals and congruences of lattices, Fuzzy Sets and Systems 95 (1998) 249-253.   DOI
23 K.L.N. Swamy and U.M. Swamy, Fuzzy prime ideals of rings , J. Math. Anal. and Appl. 134 (1988) 94-103.   DOI
24 L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353.   DOI
25 B. A. Alaba, M. A. Taye and D. A. Engidaw, L-fuzzy prime ideals and maximal L-fuzzy ideals of a poset , Ann. Fuzzy Math. Inform. 18(1) (2019) 1-13.   DOI
26 J. Larmerova and J. Rachunek, Translations of distributive and modular ordered sets , Acta. Univ. Palack. Olomuc. Fac. Rerum.Natur. Math., 91 (1988), 13-23.
27 B. A. Alaba and G. M. Addis, L-Fuzzy prime ideals in universal algebras, Advances in Fuzzy Systems, Vol. 2019, Article ID 5925036, 7 pages, 2019.
28 B.A Alaba and T.G. Alemayehu, Closure Fuzzy Ideals of MS-algebras, Ann. Fuzzy Math. Inform., 16 (2018) 247-260.   DOI
29 B.A Alaba and T.G. Alemayehu, Fuzzy ideals in demipseudocomplemented MS-algebras, Ann. Fuzzy Math. Inform., 18(2019) 123-143.   DOI
30 B. A. Alaba, M. Alamneh and D. Abeje, L-Fuzzy filters of a poset , Int. J. Comp. Sci. Appl. Math. 5(1) (2019), 23-29   DOI
31 B. A. Alaba and W. Z. Norahun, Fuzzy ideals and fuzzy filters of pseudo-complemented semi-lattices, Advances in Fuzzy Systems, vol. 2019, Article ID 4263923, 13 pages, 2019.
32 P. Das, Fuzzy vector spaces under triangular norms, Fuzzy Sets and Systems 25 (1988) 73-85.   DOI
33 V. N. Dixit, R. Kumar and N. Ajamal, On fuzzy rings, Fuzzy Sets and Systems, 49 (1992) 205-213.   DOI
34 V. N. Dixit, R. Kumar and N. Ajmal, Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy Sets and Systems, 44(1991) 127-138.   DOI
35 R. Halas, Decomposition of directed sets with zero, Math. Slovaca 45 (1) (1995) 9-17.
36 R. Halas and J.Rachunek, Polars and prime ideals in ordered sets, Discuss. Math., Algebra and Stochastic Methods 15 (1995), 43-59.
37 B. A. Alaba and W. Z. Norahun, α- fuzzy ideals and space of prime α-fuzzy ideals in distributive lattices, Ann. Fuzzy Math. Inform. 17 (2019), 147-163.   DOI
38 Y. Bo and W. Wu, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems 35 (1990), 231-240.   DOI