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Jahan, Iffat. (1388). EMBEDDING OF THE LATTICE OF IDEALS OF A RING INTO ITS LATTICE OF FUZZY IDEALS. نشریه علمی دانشگاه سیستان و بلوچستان, 6(3), 65-71. doi: 10.22111/ijfs.2009.201
Iffat Jahan. "EMBEDDING OF THE LATTICE OF IDEALS OF A RING INTO ITS LATTICE OF FUZZY IDEALS". نشریه علمی دانشگاه سیستان و بلوچستان, 6, 3, 1388, 65-71. doi: 10.22111/ijfs.2009.201
Jahan, Iffat. (1388). 'EMBEDDING OF THE LATTICE OF IDEALS OF A RING INTO ITS LATTICE OF FUZZY IDEALS', نشریه علمی دانشگاه سیستان و بلوچستان, 6(3), pp. 65-71. doi: 10.22111/ijfs.2009.201
Jahan, Iffat. EMBEDDING OF THE LATTICE OF IDEALS OF A RING INTO ITS LATTICE OF FUZZY IDEALS. نشریه علمی دانشگاه سیستان و بلوچستان, 1388; 6(3): 65-71. doi: 10.22111/ijfs.2009.201

EMBEDDING OF THE LATTICE OF IDEALS OF A RING INTO ITS LATTICE OF FUZZY IDEALS

Iranian Journal of Fuzzy Systems
مقاله 6، دوره 6، شماره 3، دی 2009، صفحه 65-71  XML اصل مقاله (161.75 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2009.201
نویسنده
Iffat Jahan email
Department of Mathematics, Ramjas College, University Of Delhi, Delhi, India
چکیده
We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzy
ideals in uncountably many ways. For this purpose, we introduce the concept of the generalized
characteristic function $\chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ for
fixed $r , s\in [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalized
characteristic function $\chi _{s}^{r} (A)$ is a fuzzy ideal of $R$. We also
show that the set of all generalized characteristic functions $C_{s}^{r}
(I(R))$ of the members of $I(R)$ for fixed $r , s\in [0,1] $ is a
complete sublattice of the lattice of all fuzzy ideals of $R$ and establish
that this latter lattice is generated by the union of all
its complete sublattices $C_{s}^{r} (I(R))$.
کلیدواژه‌ها
Algebra؛ Ideal of a ring؛ Morphism؛ Embedding؛ Lattice
مراجع
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Information Sci., 76 (1994), 1-11.
[2] T. Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and
Systems, 73 (1995), 349-358.
[3] L. Wangjin, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),
133-139.
[4] D. S. Malik and J. N. Mordeson, Radicals of fuzzy ideals, Information Sci., 65 (1992) 23,
239-252.
[5] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
[6] A. Weinberger, Embedding lattices of fuzzy subalgebras into lattices of crisp sub-algebras,
Information Sci., 108 (1998), 51-70.

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