



1
Title: On Commutator Length of Certain pGroups
Vol.39(4) (2015) page: 453459
Author(s): M. AkhavanMalayeri
Abstract: In this paper we study certain finite pgroups, in which the commutator length is equal to 1 or 2, every Coleman automorphism is inner, and the normalizer property holds.
Keywords: Commutator length; Nilpotent group; Wreath product. 
2
Title: Quotient Lattice and Its Ideals of a JPsemilattice
Vol.39(4) (2015) page: 461468
Author(s): S.N. Begum
Abstract: In this paper we study quotient JPsemilattice of a JPsemilattice. A JPsemilattice is a meet semilattice with a partial join operation satisfying some axioms. We introduce a new notion of strong filter for a JPsemilattice. We discuss the quotient lattice of a congruence containing a strong filter as a class.
Keywords: Semilattice; Distributive semilattice; Congruence; Filter; Quotient lattice. 
3
Title: Generalizations of Prime Subsemimodules
Vol.39(4) (2015) page: 469476
Author(s): M.K. Dubey and P. Sarohe
Abstract: Let S be a commutative semiring with unity and M be an unitary left Ssemimodule. Let ϕ:T(M)→ T(M)∪{∅} be a function, where T(M) is the set of all subsemimodules of M. A proper subsemimodule N of M is called a ϕprime subsemimodule of M if s ∈ S, x ∈ M, sx ∈ N\ϕ(N), then either s ∈ (N:M) or x ∈ N. In this paper, we study the concept of ϕprime subsemimodule which is a generalization of ϕprime ideal in a commutative ring and give some characterizations in terms of Msubtractive subsemimodules.
Keywords: Semiring; Semimodule; ϕprime subsemimodule; Msubtractive subsemimodule. 
4
Title: On Real Valued IConvergent ASummable Sequence Spaces Defined by Sequences of Orlicz Functions
Vol.39(4) (2015) page: 477485
Author(s): A. Esi and M.K. Ozdemir
Abstract: In this article we introduce some new sequence spaces using Iconvergence and sequences of Orlicz functions, and study some basic topological and algebraic properties of these spaces. Also we investigate the relations between these spaces.
Keywords: Ideal; Iconvergent; Orlicz function; Matrix transformation. 
5
Title: Representation Crossed Category of Weak Hopf Group Coalgebras
Vol.39(4) (2015) page: 487495
Author(s): S.J. Guo
Abstract: In this paper, we give the definitions of crossed left πHmodules over a weak crossed Hopf πcoalgebra H, and show that the category of crossed left πHmodules is a monoidal category. Finally, we show that a family R={R_{α, β} ∈ τ_{β,α}(φ_{α−1}øid_{Hα})∆_{αβα−1, α}(1_{αβ})(H_{α}øH_{β})∆_{α, β}(1_{αβ})} of elements is a quasitriangular structure of a weak crossed Hopf πcoalgebra H if and only if the category of crossed left πHmodules over H is a braided monoidal category with the braiding defined by R.
Keywords: ??Hmodules; Braided monoidal category; Quasitriangular structure. 
6
Title: Central Armendariz Condition on Monoid Rings
Vol.39(4) (2015) page: 497510
Author(s): M. Habibi
Abstract: For a monoid M, we introduce central Armendariz rings relative to M (central MArmendariz rings), which are a generalization of both MArmendariz rings and central Armendariz rings and we investigate their properties. We prove that central MArmendariz rings are abelian, but the converse is not true in general. Also for a strictly totally ordered monoid M and an ideal I of a ring R, If I is reduced (as a ring without identity) and R/I is central MArmendariz, then R is central MArmendariz. Moreover, several extensions of central MArmendariz rings are studied and various types of examples of central MArmendariz rings, extending the class of central MArmendariz rings to nonsemiprime rings are provided.
Keywords: Central MArmendariz rings; Monoid rings. 
7
Title: Strong Differential Subordination and Superordination for Analytic Functions Involving Certain Operator
Vol.39(4) (2015) page: 511527
Author(s): M.P. Jeyaraman and T.K. Suresh
Abstract: Strong differential subordination and superordination results are obtained for analytic functions in the open unit disk, which are associated with an integral operator. These results are obtained, by investigating appropriate classes of admissible functions. New strong differential sandwichtype results are also obtained.
Keywords: Strong differential subordination; Strong differential superordination; Analytic functions; Admissible functions; Hadamard product. 
8
Title: Annihilator Ideals of a Calgebra
Vol.39(4) (2015) page: 529538
Author(s): S. Kalesha Vali, P. Sundarayya and U.M. Swamy
Abstract: The notion of an annihilator ideal is introduced in a Calgebra and proved various properties. It is proved that the set ℑ(A) of all ideals of a Calgebra A is a Hayting algebra. It is known that in a Boolean algebra, every prime ideal is maximal but it is under investigation that in a Calgebra, whether every prime ideal is maximal. In this paper it is proved that in a Calgebra, every prime ideal is maximal if and only if SpecA is a hausdorff space.
Keywords: Calgebra; Annihilator ideal; Algebraic lattice; Hayting algebra; Infinite meet distributive lattice. 
9
Title: Bipartite and Planar Power Graphs of Finite Groups
Vol.39(4) (2015) page: 539543
Author(s): S.K. Maity
Abstract: The undirected power graph G(S) of a semigroup S is an undirected graph whose vertex set is S and two vertices a, b ∈ S are adjacent if and only if a ≠ b and a^{m} = b or b^{m} = a for some positive integer m. In this paper we characterize the class of finite groups S for which G(S) is bipartite. As a consequence we prove that G(U_{n}) is bipartite if and only if n = 2^{k}3^{l}; 0 ≤ k ≤ 3, 0 ≤ l ≤ 1 and n ≥ 3. Also we prove that the power graph of the multiplicative semigroup \BbbZ_{n} is bipartite if and only if n is one of 2, 3, 4, 6, 8, 12. We study a class of cyclic groups G for which G(G) is planar.
Keywords: Semigroup; Power graph; Bipartite graph; Planar graph; Chromatic number. 
10
Title: BAlmost Distributive Lattices
Vol.39(4) (2015) page: 545554
Author(s): G.C. Rao and N.K. Kakumanu
Abstract: The concept of a BAlmost Distributive Lattice (B−ADL) as a generalization of a B−algebra is introduced. Necessary and sufficient conditions for an ADL to become a B−ADL are given. Different characterizations of a B−ADL are obtained.
Keywords: Almost distributive lattice (ADL); Maximal element; Principal ideal; Birkhoff center; B−algebra; B−almost distributive lattice (B−ADL). 
11
Title: Derivations of Implicative Semilattices
Vol.39(4) (2015) page: 555566
Author(s): M. Sambasiva Rao
Abstract: The concept of derivations is introduced in an implicative semilattice. Implicative filters of direct products of implicative semilattices are characterized. A set of equivalent conditions is derived for two idempotent derivations to be equal. The concept of implicative congruences is introduced in an implicative semilattice. An interconnection between derivations and implicative congruences is obtained.
Keywords: Implicative semilattice; Derivation; Implicative filter; Kernel of a derivation; Implicative congruence. 
12
Title: Duality for Group Actions on Semialgebras
Vol.39(4) (2015) page: 567581
Author(s): R.P. Sharma and Anu
Abstract: Let R be an additively cancellative K− semialgebra, where K is an additively cancellative commutative semiring. If R is graded by G, we form the smash product R # K[G]^{∗} using the tensor product defined in [17]. On the other hand if S is a K−semialgebra and G a finite group acting on S, then the skew group ring S∗G is Ggraded and we have the smash product (S∗G) # K[G]^{∗} which is isomorphic to M_{n}(S). The identity component R_{1} plays the same role that is played by Gfixed subring in group actions. The main aim of this paper is to establish relations between the semiprimeness of R_{1}, graded semiprimeness of R and semiprimeness of R #K[G]^{∗}, when the grading is nondegenerate.
Keywords: Semigroups; Semirings; Semimodules; Semialgebras; Tensor product; Skew group ring; Semiprimeness; Nondegenerate. 
13
Title: Some Combinatorial Results on the Full Transformation Semigroup
Vol.39(4) (2015) page: 583593
Author(s): V.K. Sreeja and A.R. Rajan
Abstract: We consider the full transformation semigroup T(X) on a finite set X. This is the semigroup of all mappings from X to X under composition of mappings as the binary operation. For a finite set X, T(X) has been known to be a unit regular semigroup and strongly unit regular for X ≤ 3 [3]. We show further that T(X) is a R−strongly unit regular semigroup for a finite set X. The unit regularity of T(X) is evident in many properties of T(X) and so we give a detailed study of this semigroup and illustrate many results for this case. In this paper, we provide some combinatorial results relating to the factorization of elements of T(X) into product of idempotents and units.
Keywords: Transformation semigroup; Green's relations; Unit regular semigroup; Partitions. 
14
Title: On Partially SEmbedded Subgroups and the Supersolubility of Finite Groups
Vol.39(4) (2015) page: 595603
Author(s): T. Zhao
Abstract: Let H be a subgroup of a finite group G, we say that H is partially Sembedded in G if there exists a normal subgroup T of G such that HT is spermutable in G and H∩T ≤ H_{?DsG}, where H_{?DsG} is generated by all those subgroups of H which are ssemipermutable in G. In this paper, we investigate the influence of some partially Sembedded subgroups with prime power order on the structure of a finite group G. Some new criteria about the pnilpotency and supersolubility of a finite group were obtained. Our results also generalized some earlier ones about formations.
Keywords: spermutable subgroup; Partially Sembedded subgroup; pnilpotent group; Saturated formation. 
14 Records!





