Communications of the
Korean Mathematical Society
CKMS

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

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  • 2023-07-31

    Oriented transformations on a finite chain: another description

    Vítor Hugo Fernandes

    Abstract : Following the new description of an oriented full transformation on a finite chain given recently by Higgins and Vernitski in [4], in this short note we present a refinement of this description which is extendable to partial transformations and to injective partial transformations.

  • 2023-01-31

  • 2024-01-31

    Terminal spaces of monoids

    Amartya Goswami

    Abstract : The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to $r$-strongly irreducible $r$-ideals (endowed with Zariski topologies) of monoids, called terminal spaces. We show that terminal spaces are $T_0$, quasi-compact, and every nonempty irreducible closed subset has a unique generic point. We characterize $r$-arithmetic monoids in terms of terminal spaces. Finally, we provide necessary and sufficient conditions for the subspaces of $r$-maximal $r$-ideals and $r$-prime $r$-ideals to be dense in the corresponding terminal spaces.

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  • 2023-01-31

    Existence theorems for critical degenerate equations involving the Grushin operators

    Huong Thi Thu Nguyen, Tri Minh Nguyen

    Abstract : In this paper we prove the existence of nontrivial weak solutions to the boundary value problem \begin{align*} - G_1 u & =u^3 + f(x,y,u) \quad \text{ in } \Omega ,\\ u &\geq 0 \quad \text{ in } \Omega ,\\ u & =0 \quad \text{ on } \partial\Omega , \end{align*} where $\Omega $ is a bounded domain with smooth boundary in $\mathbb{R}^3$, $G_1 $ is a Grushin type operator, and $f(x,y,u)$ is a lower order perturbation of $u^3$ with $f(x,y,0)=0$. The nonlinearity involved is of critical exponent, which differs from the existing results in \cite{Tri:2018,TriLuyen:2020}.

  • 2024-01-31

    Nonnil-$S$-coherent rings

    Najib Mahdou, El Houssaine Oubouhou

    Abstract : Let $R$ be a commutative ring with identity. If the nilpotent radical $Nil(R)$ of $R$ is a divided prime ideal, then $R$ is called a $\phi$-ring. Let $R$ be a $\phi$-ring and $S$ be a multiplicative subset of $R$. In this paper, we introduce and study the class of nonnil-$S$-coherent rings, i.e., the rings in which all finitely generated nonnil ideals are $S$-finitely presented. Also, we define the concept of $\phi$-$S$-coherent rings. Among other results, we investigate the $S$-version of Chase's result and Chase Theorem characterization of nonnil-coherent rings. We next study the possible transfer of the nonnil-$S$-coherent ring property in the amalgamated algebra along an ideal and the trivial ring extension.

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  • 2023-04-30

    Generalized hyperbolic geometric flow

    Shahroud Azami, Ghodratallah Fasihi~Ramandi, Vahid Pirhadi

    Abstract : In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an $n$-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.

  • 2024-01-31

    Results of 3-derivations and commutativity for prime rings with involution involving symmetric and skew symmetric components

    Hanane AHARSSI, Kamal CHARRABI, Abdellah MAMOUNI

    Abstract : This article examines the connection between 3-derivations and the commutativity of a prime ring $R$ with an involution $\ast$ that fulfills particular algebraic identities for symmetric and skew symmetric elements. In practice, certain well-known problems, such as the Herstein problem, have been studied in the setting of three derivations in involuted rings.

  • 2024-04-30

    Geometric properties of starlikeness involving hyperbolic cosine function

    Om P. Ahuja, Asena Çetinkaya, Sushil Kumar

    Abstract : In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

  • 2023-01-31

    Pr\"ufer conditions vs EM conditions

    Emad Abuosba, Mariam Al-Azaizeh, Manal Ghanem

    Abstract : In this article we relate the six Pr\"{u}fer conditions with the EM conditions. We use the EM-conditions to prove some cases of equivalence of the six Pr\"{u}fer conditions. We also use the Pr\"{u}fer conditions to answer some open problems concerning EM-rings.

  • 2024-01-31

    On a uniqueness question of meromorphic functions and partial shared values

    Imrul Kaish, Rana Mondal

    Abstract : In this paper, we prove a uniqueness theorem of non-constant meromorphic functions of hyper-order less than $1$ sharing two values CM and two partial shared values IM with their shifts. Our result in this paper improves and extends the corresponding results from Chen-Lin \cite{CL2016}, Charak-Korhonen-Kumar \cite{CKK2016}, Heittokangas-Korhonen-Laine-Rieppo-Zhang \cite{HKLRZ2009} and Li-Yi \cite{LY2016}. Some examples are provided to show that some assumptions of the main result of the paper are necessary.

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October, 2024
Vol.39 No.4

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