Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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  • 2023-10-31

    On graded $(m, n)$-closed submodules

    Rezvan Varmazyar

    Abstract : Let $A$ be a $G$-graded commutative ring with identity and $M$ a graded $A$-module. Let $m, n$ be positive integers with $m>n$. A proper graded submodule $L$ of $M$ is said to be graded $(m, n)$-closed if $a^{m}_g\cdot x_t\in L$ implies that $a^{n}_g\cdot x_t\in L$, where $a_g\in h(A)$ and $x_t\in h(M)$. The aim of this paper is to explore some basic properties of these class of submodules which are a generalization of graded $(m, n)$-closed ideals. Also, we investigate $GC^{m}_n-rad$ property for graded submodules.

  • 2022-07-31

    Commutativity criteria of prime rings involving two endomorphisms

    Souad Dakir, Abdellah Mamouni, Mohammed Tamekkante

    Abstract : This paper treats the commutativity of prime rings with involution over which elements satisfy some specific identities involving endomorphisms. The obtained results cover some well-known results. We show, by given examples, that the imposed hypotheses are necessary.

  • 2022-10-31

    Certain image formulas of $(p,\nu)$--extended Gauss' hypergeometric function and related Jacobi transforms

    Purnima Chopra, Mamta Gupta, Kanak Modi

    Abstract : Our aim is to establish certain image formulas of the $ (p,\nu)$--extended Gauss' hypergeometric function $F_{\,p,\nu}(a,b;c;z)$ by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erd\'elyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the $ (p,\nu)$--extended Gauss's hypergeometric function $F_{\,p,\nu}(a,b;c;z)$ and Fox-Wright function $_{r}\Psi_{s}(z)$. We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the $ (p,\nu)$--extended Gauss' hypergeometric function $F_{\,p,\nu}(a,b;c;z)$.

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  • 2022-10-31

    Riemannian submersions whose total space is endowed with a torse-forming vector field

    \c{S}emsi Eken~Meri\c{c}, Erol K{\i}l{\i}\c{c}

    Abstract : In the present paper, a Riemannian submersion $\pi$ between Riemannian manifolds such that the total space of $\pi$ endowed with a torse-forming vector field $\nu$ is studied. Some remarkable results of such a submersion whose total space is Ricci soliton are given. Moreover, some characterizations about any fiber of $\pi$ or the base manifold $B$ to be an almost quasi-Einstein are obtained.

  • 2023-10-31

    Nonlinear maps preserving the mixed product $_*[X\diamond Y, Z]$ on $*$-algebras

    Raof Ahmad Bhat, Abbas Hussain Shikeh, Mohammad Aslam Siddeeque

    Abstract : Let $\mathfrak{A}$ and $\mathfrak{B}$ be unital prime $*$-algebras such that $\mathfrak{A}$ contains a nontrivial projection. In the present paper, we show that if a bijective map $\Theta:\mathfrak{A}\to\mathfrak{B}$ satisfies $\Theta(_*[X\diamond Y, Z])={}_*[\Theta(X)\diamond \Theta(Y), \Theta(Z)]$ for all $X, Y, Z\in\mathfrak{A}$, then $\Theta$ or $-\Theta$ is a $*$-ring isomorphism. As an application, we shall characterize such maps in factor von Neumann algebras.

  • 2023-07-31

    Convergence of sequences in generalized topological spaces via filter

    Julio C. Ramos-Fernández, Ennis Rosas, Margot Salas-Brown

    Abstract : In this paper a generalization of convergent sequences in connection with generalized topologies and filters is given. Additionally, properties such as uniqueness, behavior related to continuous functions are established and notions relative to product spaces.

  • 2023-07-31

    Certain study of generalized $B$ curvature tensor within the framework of Kenmotsu manifold

    Rahuthanahalli Thimmegowda Naveen Kumar, Basavaraju Phalaksha Murthy, Puttasiddappa Somashekhara, Venkatesha Venkatesha

    Abstract : In the present study, we consider some curvature properties of generalized $B$-curvature tensor on Kenmotsu manifold. Here first we describe certain vanishing properties of generalized $B$ curvature tensor on Kenmostu manifold. Later we formulate generalized $B$ pseudo-symmetric condition on Kenmotsu manifold. Moreover, we also characterize generalized $B$ $\phi$-recurrent Kenmotsu manifold.

  • 2022-10-31

    On the semi-local convergence of contraharmonic-mean Newton's method (CHMN)

    Ioannis K. Argyros, Manoj Kumar Singh

    Abstract : The main objective of this work is to investigate the study of the local and semi-local convergence of the contraharmonic-mean Newton's method (CHMN) for solving nonlinear equations in a Banach space. We have performed the semi-local convergence analysis by using generalized conditions. We examine the theoretical results by comparing the CHN method with the Newton's method and other third order methods by Weerakoon et al.~using some test functions. The theoretical and numerical results are also supported by the basins of attraction for a selected test function.

  • 2022-10-31

    Golden para-contact metric manifolds

    Gherici Beldjilali, Habib Bouzir

    Abstract : The purpose of the present paper is to introduce a new class of almost para-contact metric manifolds namely, Golden para-contact metric manifolds. Then, we are particularly interested in a more special type called Golden para-Sasakian manifolds, where we will study their fundamental properties and we present many examples which justify their study.

  • 2023-07-31

    Local-global principle and generalized local cohomology modules

    Bui Thi Hong Cam, Nguyen Minh Tri, Do Ngoc Yen

    Abstract : Let $\mathcal{M}$ be a stable Serre subcategory of the category of $R$-modules. We introduce the concept of $\mathcal{M}$-minimax $R$-modules and investigate the local-global principle for generalized local cohomology modules that concerns to the $\mathcal{M}$-minimaxness. We also provide the $\mathcal{M}$-finiteness dimension $f^{\mathcal{M}}_I(M,N)$ of $M,N$ relative to $I$ which is an extension the finiteness dimension $f_I(N)$ of a finitely generated $R$-module $N$ relative to $I$.

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April, 2024
Vol.39 No.2

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