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TitleOn Generalized (??,??)-n-Derivations in Rings
Vol.40(6) (2016) page: 783-796
Author(s): M. Ashraf and N. Parveen  

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)-n-derivation G of a prime or semiprime ring R associated with a permuting (α,β)-n-derivation 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 α-left n-centralizer or R is commutative. Further, some more related results have also been obtained.

Keywords: Semiprime-rings; Derivations; Permuting n-derivations; Permuting generalized (??,??)-n-derivations; trace of permuting (??,??) n-derivations.
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TitleSome Arithmetical Results on Reciprocal Sums of Certain Fibonacci-Type Numbers
Vol.40(6) (2016) page: 797-814
Author(s): P. Bundschuh and K. Vääanänen  

First, closed form evaluations of series generalizing ∑1/F2k, are resumed. Next, transcendence proofs of ∑1/Fdk for integers d > 2 by Roth's approximation theorem, or by Mahler's analytic method are recalled. This second method leads to far-reaching transcendence and algebraic independence results on series, where the Fibonaccis Fn 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.
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TitleDistribution of Prime Ideals in Subalgebras of C(X)
Vol.40(6) (2016) page: 815-822
Author(s): D. De   

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 non-maximal prime ideal and the unique maximal ideal extending it constitutes a Dedekind complete chain with atleast 21 many members. A special case of this result with A(X)=C(X) (respectively C*(X)) is already covered in Gillman-Jerison text. From this it follows that if A(X) ≠ C(X) then there are atleast 21 many non-maximal 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.
Size:119KB   download
TitleThe Triple ?? of Ideal Fuzzy Real Numbers Over p-Metric Spaces Defined by Musielak Orlicz Function
Vol.40(6) (2016) page: 823-836
Author(s): Deepmala, N. Subramanian and L.N. Mishra  

In this article we introduce the sequence spaces [χ3FIf ,||(d(x1),d(x2),…,d(xn−1))||p] and [Λ3FIf ,||(d(x1),d(x2),…, d(xn−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 p-metric space; Fuzzy number; Solid space; Symmetricity; Convergence free; Sequence algebra; Ideal.
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TitlePoisson Summation and Endoscopy for Sp(4,R)
Vol.40(6) (2016) page: 837-856
Author(s): D.N. Diep and D.T.P. Quynh  

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.
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TitleNeighborhood for a Subclass of Meromorphically p-Valent Functions
Vol.40(6) (2016) page: 857-863
Author(s): B.A. Frasin and T. Al-Hawary   

In the present paper, we introduce a new definition of neighborhood for subclass M(α,β,δ,p;g) of meromorphically p-valent functions. Furthermore, we obtain some interesting results for this subclass. An application of Jack's lemma is also given.

Keywords: Analytic functions; Meromorphically p-valent functions; Neighborhood.
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Title-Subideal and -Subabideal Subalgebras of Finite Dimensional Lie Algebras
Vol.40(6) (2016) page: 865-874
Author(s): L. Goudarzi, Z. Riyahi and A.R. Salemkar  

In the article, we introduce the concepts of \mathfrakF-subideal and \mathfrakF-subabideal 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 \mathfrakF-subideal or \mathfrakF-subabideal in L, and all Lie algebras L for which every subalgebra is \mathfrakF-subabideal in a \mathfrakF-subideal subalgebra of L are characterized.

Keywords: Lie algebra; \mathfrakF-covering subalgebra; \mathfrakF-projector; \mathfrakF-subideal; \mathfrakF-subabideal.
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TitleOn Multi-Granular Nano Topology
Vol.40(6) (2016) page: 875-885
Author(s): M. Lellis Thivagar and V. Sutha Devi  

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; Multi-lower approximation; Multi-upperapproximation; Multi-boundary; Multigranular nano topology in terms of union; Nano measure.
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TitleRetractable and Coretractable Acts Over Semigroups
Vol.40(6) (2016) page: 887-903
Author(s): M.A. Naghipoor and M. Ershad  

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.
Size:167KB   download
TitleSome Lp Inequalities Concerning the Polar Derivative of a Polynomial
Vol.40(6) (2016) page: 905-910
Author(s): N.A. Rather, S. Gulzar and K.A. Thakur  

For the class of lacunary polynomials P(z)=anzn+∑ν = μnan−νzn−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| ≥ kμ,

\underset|z|=1 max |Dα P(z)| ≥ n


\underset|z|=1 max |P(z)|+ n(|α|+1)

\underset|z|=k min |P(z)|

where Dα 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 Lp mean extension of above inequality.

Keywords: Polynomials; Inequalities in the complex domain; Polar derivative.
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TitleA Class of General Type of Regularities and Generalized Semiprime Ideals in Ternary Ring
Vol.40(6) (2016) page: 911-922
Author(s): Md. Salim and T.K. Dutta  

In this paper we introduce the notion of general type of regularities for ternary rings. We also introduce the notions of Von-Neumann regularity, D-regularity, λ-regularity, f-regularity 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: Von-Neumann regularity; Semiprime ideal.
Size:123KB   download
TitleProperties of Completely Regular Semirings
Vol.40(6) (2016) page: 923-930
Author(s): N. Sulochana and T. Vasanthi  

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.
Size:83KB   download
Title Contents for Volume 40
Vol.40(6) (2016) page: 931-935
Size:51KB   download
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