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TitleOn Commutator Length of Certain p-Groups
Vol.39(4) (2015) page: 453-459
Author(s): M. Akhavan-Malayeri  

In this paper we study certain finite p-groups, 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.
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TitleQuotient Lattice and Its Ideals of a JP-semilattice
Vol.39(4) (2015) page: 461-468
Author(s): S.N. Begum  

In this paper we study quotient JP-semilattice of a JP-semilattice. A JP-semilattice is a meet semilattice with a partial join operation satisfying some axioms. We introduce a new notion of strong filter for a JP-semilattice. We discuss the quotient lattice of a congruence containing a strong filter as a class.

Keywords: Semilattice; Distributive semilattice; Congruence; Filter; Quotient lattice.
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TitleGeneralizations of Prime Subsemimodules
Vol.39(4) (2015) page: 469-476
Author(s): M.K. Dubey and P. Sarohe  

Let S be a commutative semiring with unity and M be an unitary left S-semimodule. 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 ϕ-prime 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 ϕ-prime subsemimodule which is a generalization of ϕ-prime ideal in a commutative ring and give some characterizations in terms of M-subtractive subsemimodules.

Keywords: Semiring; Semimodule; ϕ-prime subsemimodule; M-subtractive subsemimodule.
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TitleOn Real Valued I-Convergent A-Summable Sequence Spaces Defined by Sequences of Orlicz Functions
Vol.39(4) (2015) page: 477-485
Author(s): A. Esi and M.K. Ozdemir  

In this article we introduce some new sequence spaces using I-convergence 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; I-convergent; Orlicz function; Matrix transformation.
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TitleRepresentation Crossed Category of Weak Hopf Group Coalgebras
Vol.39(4) (2015) page: 487-495
Author(s): S.J. Guo  

In this paper, we give the definitions of crossed left π-H-modules over a weak crossed Hopf π-coalgebra H, and show that the category of crossed left π-H-modules is a monoidal category. Finally, we show that a family R={Rα, β ∈ τβ,αα−1øidHα)∆αβα−1, α(1αβ)(HαøHβ)∆α, β(1αβ)} of elements is a quasitriangular structure of a weak crossed Hopf π-coalgebra H if and only if the category of crossed left π-H-modules over H is a braided monoidal category with the braiding defined by R.

Keywords: ??-H-modules; Braided monoidal category; Quasitriangular structure.
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TitleCentral Armendariz Condition on Monoid Rings
Vol.39(4) (2015) page: 497-510
Author(s): M. Habibi  

For a monoid M, we introduce central Armendariz rings relative to M (central M-Armendariz rings), which are a generalization of both M-Armendariz rings and central Armendariz rings and we investigate their properties. We prove that central M-Armendariz 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 M-Armendariz, then R is central M-Armendariz. Moreover, several extensions of central M-Armendariz rings are studied and various types of examples of central M-Armendariz rings, extending the class of central M-Armendariz rings to non-semiprime rings are provided.

Keywords: Central M-Armendariz rings; Monoid rings.
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TitleStrong Differential Subordination and Superordination for Analytic Functions Involving Certain Operator
Vol.39(4) (2015) page: 511-527
Author(s): M.P. Jeyaraman and T.K. Suresh  

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 sandwich-type results are also obtained.

Keywords: Strong differential subordination; Strong differential superordination; Analytic functions; Admissible functions; Hadamard product.
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TitleAnnihilator Ideals of a C-algebra
Vol.39(4) (2015) page: 529-538
Author(s): S. Kalesha Vali, P. Sundarayya and U.M. Swamy  

The notion of an annihilator ideal is introduced in a C-algebra and proved various properties. It is proved that the set ℑ(A) of all ideals of a C-algebra 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 C-algebra, whether every prime ideal is maximal. In this paper it is proved that in a C-algebra, every prime ideal is maximal if and only if SpecA is a hausdorff space.

Keywords: C-algebra; Annihilator ideal; Algebraic lattice; Hayting algebra; Infinite meet distributive lattice.
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TitleBipartite and Planar Power Graphs of Finite Groups
Vol.39(4) (2015) page: 539-543
Author(s): S.K. Maity  

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 am = b or bm = 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(Un) is bipartite if and only if n = 2k3l; 0 ≤ k ≤ 3, 0 ≤ l ≤ 1 and n ≥ 3. Also we prove that the power graph of the multiplicative semigroup \BbbZn 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.
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TitleB-Almost Distributive Lattices
Vol.39(4) (2015) page: 545-554
Author(s): G.C. Rao and N.K. Kakumanu  

The concept of a B-Almost 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).
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TitleDerivations of Implicative Semi-lattices
Vol.39(4) (2015) page: 555-566
Author(s): M. Sambasiva Rao  

The concept of derivations is introduced in an implicative semi-lattice. Implicative filters of direct products of implicative semi-lattices 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 semi-lattice. An interconnection between derivations and implicative congruences is obtained.

Keywords: Implicative semi-lattice; Derivation; Implicative filter; Kernel of a derivation; Implicative congruence.
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TitleDuality for Group Actions on Semialgebras
Vol.39(4) (2015) page: 567-581
Author(s): R.P. Sharma and Anu  

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 G-graded and we have the smash product (S∗G) # K[G] which is isomorphic to Mn(S). The identity component R1 plays the same role that is played by G-fixed subring in group actions. The main aim of this paper is to establish relations between the semiprimeness of R1, 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.
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TitleSome Combinatorial Results on the Full Transformation Semigroup
Vol.39(4) (2015) page: 583-593
Author(s): V.K. Sreeja and A.R. Rajan  

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.
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TitleOn Partially S-Embedded Subgroups and the Supersolubility of Finite Groups
Vol.39(4) (2015) page: 595-603
Author(s): T. Zhao  

Let H be a subgroup of a finite group G, we say that H is partially S-embedded in G if there exists a normal subgroup T of G such that HT is s-permutable in G and H∩T ≤ H?DsG, where H?DsG is generated by all those subgroups of H which are s-semipermutable in G. In this paper, we investigate the influence of some partially S-embedded subgroups with prime power order on the structure of a finite group G. Some new criteria about the p-nilpotency and supersolubility of a finite group were obtained. Our results also generalized some earlier ones about formations.

Keywords: s-permutable subgroup; Partially S-embedded subgroup; p-nilpotent group; Saturated formation.
Size:125KB   download
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