



1
Title: On Generalized (??,??)nDerivations in Rings
Vol.40(6) (2016) page: 783796
Author(s): M. Ashraf and N. Parveen
Abstract: Let R be a ring with center Z(R), α, β be endomorphisms of R. In the present paper we investigate some properties of permuting generalized (α,β)nderivation G of a prime or semiprime ring R associated with a permuting (α,β)nderivation D of R. Among some other results, we show that on a semiprime ring R if the trace g of G satisfies [g(x),α(x)]=0 for all x ∈ R, then the trace d of D maps R into Z(R). We also show that if the same condition is satisfied by g on prime ring then either G becomes an αleft ncentralizer or R is commutative. Further, some more related results have also been obtained.
Keywords: Semiprimerings; Derivations; Permuting nderivations; Permuting generalized (??,??)nderivations; trace of permuting (??,??) nderivations. 
2
Title: Some Arithmetical Results on Reciprocal Sums of Certain FibonacciType Numbers
Vol.40(6) (2016) page: 797814
Author(s): P. Bundschuh and K. Vääanänen
Abstract: First, closed form evaluations of series generalizing ∑1/F_{2k}, are resumed. Next, transcendence proofs of ∑1/F_{dk} for integers d > 2 by Roth's approximation theorem, or by Mahler's analytic method are recalled. This second method leads to farreaching transcendence and algebraic independence results on series, where the Fibonaccis F_{n} are replaced by more general expressions. These questions, making up the greatest part of the work, include studies of the transcendence over \mathbbC(z) of the solutions of certain functional equations.
Keywords: Transcendence; Algebraic independence; Mahler's method. 
3
Title: Distribution of Prime Ideals in Subalgebras of C(X)
Vol.40(6) (2016) page: 815822
Author(s): D. De
Abstract: Let X be a completely regular Hausdorff topological space and ∑(X) the class of all subalgebras of C(X) containing C^{*}(X). Byun and Watson published a paper in Topology and its Application in 1991, some of whose results had been corrected in the Doctoral Dissertation of present author and reproved recently by Acharyya and Bose in a paper of Topology and its Application. In the present article we prove that the class of all prime ideals in an intermediate ring A(X) that lie between a nonmaximal prime ideal and the unique maximal ideal extending it constitutes a Dedekind complete chain with atleast 2^{ℵ1} many members. A special case of this result with A(X)=C(X) (respectively C^{*}(X)) is already covered in GillmanJerison text. From this it follows that if A(X) ≠ C(X) then there are atleast 2^{ℵ1} many nonmaximal prime ideals in A(X). This generalizes a well known fact established by Gillman and Henriksen longtime ago and also sharpens a corresponding recent result of Acharyya and Bose.
Keywords: Rings of continuous functions; Prime ideals; Maximal ideals. 
4
Title: The Triple ?? of Ideal Fuzzy Real Numbers Over pMetric Spaces Defined by Musielak Orlicz Function
Vol.40(6) (2016) page: 823836
Author(s): Deepmala, N. Subramanian and L.N. Mishra
Abstract: In this article we introduce the sequence spaces [χ^{3FI}_{f },(d(x_{1}),d(x_{2}),…,d(x_{n−1}))_{p}] and [Λ^{3FI}_{f },(d(x_{1}),d(x_{2}),…, d(x_{n−1}))_{p}], and study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces and some of their properties like solidity, symmetricity, convergence free etc., and also investigate some inclusion relations related to these spaces.
Keywords: Analytic sequence; Double sequences; ??3FI space; Musielak  Orlicz function; Fuzzy pmetric space; Fuzzy number; Solid space; Symmetricity; Convergence free; Sequence algebra; Ideal. 
5
Title: Poisson Summation and Endoscopy for Sp(4,R)
Vol.40(6) (2016) page: 837856
Author(s): D.N. Diep and D.T.P. Quynh
Abstract: In this paper we analyze the endoscopy for \operatornameSp\noindentlimits(4,\mathbb R). We make a precise realization of the discrete series representations (in Section 2), a computation of their traces (Section 3) and an exact formula for the noncommutative Poisson summation and endoscopy of for this group (in Sections 4,5).
Keywords: Trace formula; Orbital integral; Transfer; Endoscopy. 
6
Title: Neighborhood for a Subclass of Meromorphically pValent Functions
Vol.40(6) (2016) page: 857863
Author(s): B.A. Frasin and T. AlHawary
Abstract: In the present paper, we introduce a new definition of neighborhood for subclass M(α,β,δ,p;g) of meromorphically pvalent functions. Furthermore, we obtain some interesting results for this subclass. An application of Jack's lemma is also given.
Keywords: Analytic functions; Meromorphically pvalent functions; Neighborhood. 
7
Title: Subideal and Subabideal Subalgebras of Finite Dimensional Lie Algebras
Vol.40(6) (2016) page: 865874
Author(s): L. Goudarzi, Z. Riyahi and A.R. Salemkar
Abstract: In the article, we introduce the concepts of \mathfrakFsubideal and \mathfrakFsubabideal subalgebras of a Lie algebra with respect to a formation \mathfrakF and investigate some properties of such subalgebras. Also, all Lie algebras L every subalgebra of which is \mathfrakFsubideal or \mathfrakFsubabideal in L, and all Lie algebras L for which every subalgebra is \mathfrakFsubabideal in a \mathfrakFsubideal subalgebra of L are characterized.
Keywords: Lie algebra; \mathfrakFcovering subalgebra; \mathfrakFprojector; \mathfrakFsubideal; \mathfrakFsubabideal. 
8
Title: On MultiGranular Nano Topology
Vol.40(6) (2016) page: 875885
Author(s): M. Lellis Thivagar and V. Sutha Devi
Abstract: This paper designs a new type of Multiple granulation nano topological theory called Multigranular nano topology. There is also an endeavour to study its properties based on their approximations. The intention is to classify the type of Multigranular nano topology based on the intrinsic structure of sets. In order to enlighten our Multigranular nano topological model some examples are considered, which are helpful for applying this theory in practical issues.
Keywords: Multigranular nano topology; Multilower approximation; Multiupperapproximation; Multiboundary; Multigranular nano topology in terms of union; Nano measure. 
9
Title: Retractable and Coretractable Acts Over Semigroups
Vol.40(6) (2016) page: 887903
Author(s): M.A. Naghipoor and M. Ershad
Abstract: Let S be a monoid. A right S−act A is said to be retractable if for each subact B of A, Hom(A,B) ≠ ∅. In this paper we define an S−act A to be coretractable if Hom(A/B,A) ≠ {0}, for every proper subact B of A. Our objective is to characterize retractable and coretractable acts by properties of underlying sets and monoids and investigate the relation between these properties of acts with some "projective or injective likes" properties. Clearly every generator is retractable and every cogenerator is coretractable in the category of S−acts. It turns out that for a monoid S with a left zero all free acts are coretractable if and only if Hom(A,S) ≠ {0}, for each S−act A.
Keywords: Retractable act; Coretractable act. 
10
Title: Some Lp Inequalities Concerning the Polar Derivative of a Polynomial
Vol.40(6) (2016) page: 905910
Author(s): N.A. Rather, S. Gulzar and K.A. Thakur
Abstract: For the class of lacunary polynomials P(z)=a_{n}z^{n}+∑_{ν = μ}^{n}a_{n−ν}z^{n−ν}, 1 ≤ μ ≤ n, of degree n having all their zeros in z ≤ k where k ≤ 1, Rather and Mir [12] proved that for α ∈ \mathbbC with α ≥ k^{μ},
\undersetz=1 
max 
D_{α} P(z) ≥ n 
⎛
⎝ 
α−k^{μ}
1+k^{μ} 
⎞
⎠ 
\undersetz=1 
max 
P(z)+ 
n(α+1)
k^{n−μ}(1+k^{μ}) 
\undersetz=k 
min 
P(z) 

where D_{α} P(z)=nP(z)+(α−z)P^{′}(z) denote the polar derivative of the polynomial P(z) of degree n with respect to a point α ∈ \mathbbC. In this paper, we obtain L_{p} mean extension of above inequality.
Keywords: Polynomials; Inequalities in the complex domain; Polar derivative. 
11
Title: A Class of General Type of Regularities and Generalized Semiprime Ideals in Ternary Ring
Vol.40(6) (2016) page: 911922
Author(s): Md. Salim and T.K. Dutta
Abstract: In this paper we introduce the notion of general type of regularities for ternary rings. We also introduce the notions of VonNeumann regularity, Dregularity, λregularity, fregularity etc. in ternary rings. Lastly we introduce generalized semiprime ideals corresponding to each of the above regularities in ternary rings and obtain some characterizations of them.
Keywords: VonNeumann regularity; Semiprime ideal. 
12
Title: Properties of Completely Regular Semirings
Vol.40(6) (2016) page: 923930
Author(s): N. Sulochana and T. Vasanthi
Abstract: In this paper, we extend the concept of completely regular semirings and study some properties. Also we prove that, if S is a completely regular semiring and S is almost idempotent semiring, then S is an idempotent semiring.
Keywords: Completely regular semigroups; Completely regular semirings; Additive reducts. 
13
Title: Contents for Volume 40
Vol.40(6) (2016) page: 931935
Author(s):
Abstract:
Keywords: 
13 Records!





