131 research outputs found
Intra regular Abel-Grassmann's groupoids characterized by their intuitionistic fuzzy ideals
In this paper, we have discussed the properties of intuitionistic fuzzy
ideals of an AG-groupoids. We have characterized an intra-regular AG-groupoid
in terms of intuitionistic fuzzy left (right, two-sided) ideals, fuzzy
(generalized) bi-ideals, intuitionistic fuzzy interior ideals and
intuitionistic fuzzy quasi ideals. We have proved that the intuitionistic fuzzy
left (right, interior, quasi) ideal coincides in an intra-regular AG-groupoid.
We have also shown that the set of intuitionistic fuzzy two-sided ideals of an
intra-regular AG-groupoid forms a semilattice structure
On fuzzy-{\Gamma}-ideals of {\Gamma}-Abel-Grassmann's groupoids
In this paper, we have introduced the notion of {\Gamma}-fuzzification in
{\Gamma}-AG-groupoids which is in fact the generalization of fuzzy
AG-groupoids. We have studied several properties of an intra-regular
{\Gamma}-AG^{**}-groupoids in terms of fuzzy {\Gamma}-left (right, two-sided,
quasi, interior, generalized bi-, bi-) ideals. We have proved that all fuzzy
{\Gamma}-ideals coincide in intra-regular {\Gamma}-AG^{**}-groupoids. We have
also shown that the set of fuzzy {\Gamma}-two-sided ideals of an intra-regular
{\Gamma}-AG^{**}-groupoid forms a semilattice structure
Characterizations of Abel-Grassmann's groupoids by their intuitionistic fuzzy ideals
In this paper, we have introduced the concept of intuitionistic fuzzy ideals
in an AG-groupoids. We have characterized regular and intra-regular
AG-groupoids in terms of intuitionistic fuzzy left (right, two-sided) ideals,
fuzzy (generalized) bi-ideals and intuitionistic fuzzy (1,2)-ideals. We have
proved that all the intuitionistic fuzzy ideals coincides in regular and
intra-regular AG-groupoids. It has been shown that the set of intuitionistic
fuzzy two sided ideals of a regular AG-groupoid forms a semilattice structure.
We have also given some useful conditions for an AG-groupoid to become an
intra-regular AG-groupoid in terms their intuitionistic fuzzy ideals
Ideals in intra-regular left almost semigroups
In this paper, we have introduced the notion of (1,2)-ideal in an
LA-semigroup and shown that (1,2)-ideal and two-sided ideal coincide in an
intra-regular LA-semigroup. We have characterized an intra-regular LA-semigroup
by using the properties of left and right ideals. Some natural examples of
LA-semigroups have been given. Further we have investigated some useful
conditions for an LA-semigroup to become an intra-regular LA-semigroup and
given the counter examples to illustrate the converse inclusions. All the
ideals (left, right, two-sided, interior, quasi, bi- generalized bi- and (1,2))
of an intra-regular LA-semigroup have been characterized. Finally we have given
an equivalent statement for a two-sided ideal of an intra-regular LA-semigroup
in terms of the intersection of two minimal two-sided ideals of an
intra-regular LA-semigroup
Characterizations of intra-regular gamma AG-groupoids by the properties of their gamma ideals
We have characterized an intra-regular {\Gamma}-AG^{**}-groupoids by using
the properties of {\Gamma}-ideals (left, right, two-sided ), {\Gamma}-interior,
{\Gamma}-quasi, {\Gamma}-bi and {\Gamma}-generalized bi and {\Gamma}-(1,2)). We
have prove that all the {\Gamma}-ideals coincides in an intra-regular
{\Gamma}-AG^{**}-groupoids. It has been examined that all the {\Gamma}-ideals
of an intra-regular {\Gamma}-AG^{**}-groupoids are {\Gamma}-idempotent. In this
paper we define all {\Gamma}-ideals in {\Gamma}-AG^{**}-groupoids and we
generalize some results
Fuzzy Abel Grassmann's Groupoids
In the present paper we have studied the concept of fuzzification in
AG-groupoids. The equivalent statement for an AG-groupoid to be a commutative
semigroup is proved. Fuzzy points have been defined in an AG-groupoid and has
been shown the representation of smallest fuzzy left ideal generated by a fuzzy
point. The set of all fuzzy left ideals, which are idempotents, forms a
commutative monoid. The relation of fuzzy left(right) ideals, fuzzy interior
ideals and fuzzy bi-ideals in AG-groupoid has been studied. Necessary and
sufficient condition of fully fuzzy prime AG-groupoid has been shown. Further,
It has been shown that the set of fuzzy quasi-prime ideals of AG-groupoid with
left identity forms a semillattice structure. Moreover, equivalent statements
for fuzzy semiprime left ideal in an AG-groupoid have been proved.Comment: 9 page
Intra-regular Abel-Grassmann's groupoids
We characterize intra-regular Abel-Grassmann's groupoids by the properties of
their ideals and -fuzzy ideals of various types
A Direct Approach to the Electromagnetic Casimir Energy in a Rectangular Waveguide
In this paper we compute the leading order Casimir energy for the
electromagnetic field (EM) in an open ended perfectly conducting rectangular
waveguide in three spatial dimensions by a direct approach. For this purpose we
first obtain the second quantized expression for the EM field with boundary
conditions which would be appropriate for a waveguide. We then obtain the
Casimir energy by two different procedures. Our main approach does not contain
any analytic continuation techniques. The second approach involves the routine
zeta function regularization along with some analytic continuation techniques.
Our two approaches yield identical results. This energy has been calculated
previously for the EM field in a rectangular waveguide using an indirect
approach invoking analogies between EM fields and massless scalar fields, and
using complicated analytic continuation techniques, and the results are
identical to ours. We have also calculated the pressures on different sides and
the total Casimir energy per unit length, and plotted these quantities as a
function of the cross-sectional dimensions of the waveguide. We also present a
physical discussion about the rather peculiar effect of the change in the sign
of the pressures as a function of the shape of the cross-sectional area.Comment: 16 pages, 6 figures, iopart style, submitted to J. Phys. B: At. Mol.
Op
Topological Structure on Abel-Grassmann's Groupoids
In this paper we have discussed the ideals in Abel Grassmann's groupoids and
construct their topologies.Comment: 5page
Abel-Grassmann's groupoids characterized by (\in ,\in \vee q_{k}) fuzzy bi-ideals
Using the idea of a quasi-coincedece of a fuzzy point with a fuzzy set, the
concept of an ({\alpha},{\beta})-fuzzy bi-ibeals in AG-groupoid is introduced
in this paper, which is a generalization of the concept of a fuzzy bi-ideal in
AG-groupoid and some interesting characterizations theorems are obtained
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