Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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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 MAMOUNIAbstract : 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.
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2023-01-31
Representations of $C^{\ast}$-ternary rings
Arpit Kansal, Ajay Kumar, Vandana RajpalAbstract : It is proved that there is a one to one correspondence between representations of $C^{\ast}$-ternary ring $M$ and $C^{\ast}$-algebra $\mathcal{A}(M)$. We discuss primitive and modular ideals of a $C^{\ast}$-ternary ring and prove that a closed ideal $I$ is primitive or modular if and only if so is the ideal $\mathcal{A}(I)$ of $\mathcal{A}(M)$. We also show that a closed ideal in $M$ is primitive if and only if it is the kernel of some irreducible representation of $M$. Lastly, we obtain approximate identity characterization of strongly quasi-central $C^{\ast}$-ternary ring and the ideal structure of the TRO $ V\otimes^{\text{\rm tmin}} B$ for a $C^{\ast}$-algebra $B$.
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2023-10-31
on weakly cyclic generalized $B$-symmetric manifolds
Mohabbat Ali, Aziz Ullah Khan, Quddus Khan, Mohd VasiullaAbstract : The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized $B$-symmetric manifold $(WCGBS)_{n}$. We obtain a sufficient condition for a weakly cyclic generalized $B$-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized $B$-symmetric manifolds. Then we study Einstein $(WCGBS)_{n}$ $(n>2)$. Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.
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2024-01-31
Some remarks on $S$-valuation domains
Ali Benhissi, Abdelamir DabbabiAbstract : Let $A$ be a commutative integral domain with identity element and $S$ a multiplicatively closed subset of $A$. In this paper, we introduce the concept of $S$-valuation domains as follows. The ring $A$ is said to be an $S$-valuation domain if for every two ideals $I$ and $J$ of $A$, there exists $s\in S$ such that either $sI\subseteq J$ or $sJ\subseteq I$. We investigate some basic properties of $S$-valuation domains. Many examples and counterexamples are provided.
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2023-10-31
Multiplicity results of critical local equation related to the genus theory
M. Alimohammady, A. Rezvani, C. TuncAbstract : Using variational methods, Krasnoselskii's genus theory and symmetric mountain pass theorem, we introduce the existence and multiplicity of solutions of a parameteric local equation. At first, we consider the following equation \[ \begin{cases} -div [a(x, |\nabla u|) \nabla u] = \mu (b(x) |u|^{s(x) -2} - |u|^{r(x) -2})u & \text{in} ~~\Omega,\\ u=0 & \text{on}~~ \partial \Omega, \end{cases} \] where $\Omega \subseteq \mathbb{R}^N$ is a bounded domain, $\mu$ is a positive real parameter, $p$, $r$ and $s$ are continuous real functions on $\bar{\Omega}$ and $a(x, \xi)$ is of type $|\xi|^{p(x) -2}$. Next, we study boundedness and simplicity of eigenfunction for the case $a(x, |\nabla u|) \nabla u= g(x) | \nabla u|^{p(x) -2}\nabla u$, where $g\in L^{\infty}(\Omega)$ and $g(x) \geq 0$ and the case $a(x, |\nabla u|) \nabla u= (1+ \nabla u|^2)^{\frac{p(x) -2}{2}} \nabla u$ such that $p(x) \equiv p$.
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2024-01-31
Terminal spaces of monoids
Amartya GoswamiAbstract : 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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2023-07-31
Riemann solitons on $(\kappa, \mu)$-almost cosymplectic manifolds
Prakasha Doddabhadrappla Gowda, Devaraja Mallesha Naik, Amruthalakshmi Malleshrao Ravindranatha, Venkatesha VenkateshaAbstract : In this paper, we study almost cosymplectic manifolds with nullity distributions admitting Riemann solitons and gradient almost Riemann solitons. First, we consider Riemann soliton on $(\kappa, \mu)$-almost cosymplectic manifold $M$ with $\kappa<0$ and we show that the soliton is expanding with $\lambda = \frac{\kappa}{2n-1}(4n-1)$ and $M$ is locally isometric to the Lie group $G_\rho$. Finally, we prove the non-existence of gradient almost Riemann soliton on a $(\kappa, \mu)$-almost cosymplectic manifold of dimension greater than 3 with $\kappa < 0$.
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2023-04-30
General system of multi-sextic mappings and stability results
Abasalt BodaghiAbstract : In this study, we characterize the structure of the multivariable mappings which are sextic in each component. Indeed, we unify the general system of multi-sextic functional equations defining a multi-sextic mapping to a single equation. We also establish the Hyers-Ulam and G\u{a}vru\c{t}a stability of multi-sextic mappings by a fixed point theorem in non-Archimedean normed spaces. Moreover, we generalize some known stability results in the setting of quasi-$\beta$-normed spaces. Using a characterization result, we indicate an example for the case that a multi-sextic mapping is non-stable.
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2024-01-31
On a uniqueness question of meromorphic functions and partial shared values
Imrul Kaish, Rana MondalAbstract : 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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2023-10-31
Analytic functions with conic domains associated with certain generalized $q$-integral operator
OM P. AHUJA, Asena \c{C}etinkaya, NAVEEN KUMAR JAINAbstract : In this paper, we define a new subclass of $k$-uniformly starlike functions of order $\gamma~ (0\leq\gamma<1)$ by using certain generalized $q$-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate $q$-sufficient coefficient condition, $q$-Fekete-Szeg\"{o} inequalities, $q$-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of $k$-uniformly convex functions of order $\gamma$ by using the generalized $q$-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.
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The measurability of Hewitt-Stromberg measures and dimensions
Zied Douzi, Bilel Selmi, Haythem Zyoudi
Commun. Korean Math. Soc. 2023; 38(2): 491-507
https://doi.org/10.4134/CKMS.c220154 -
On strong exponential limit shadowing property
Ali Darabi
Commun. Korean Math. Soc. 2022; 37(4): 1249-1258
https://doi.org/10.4134/CKMS.c210394 -
Common fixed point results for generalized orthogonal $F$-Suzuki contraction for family of multivalued mappings in orthogonal $b$-metric spaces
Bahru Tsegaye Leyew, Oluwatosin Temitope Mewomo
Commun. Korean Math. Soc. 2022; 37(4): 1147-1170
https://doi.org/10.4134/CKMS.c210410 -
On nonnil-SFT rings
Ali Benhissi, Abdelamir Dabbabi
Commun. Korean Math. Soc. 2023; 38(3): 663-677
https://doi.org/10.4134/CKMS.c220230
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Uniqueness of meromorphic function with its $k$-th derivative sharing two small functions under different weights
Abhijit Banerjee, Arpita Kundu
Commun. Korean Math. Soc. 2023; 38(2): 525-545
https://doi.org/10.4134/CKMS.c220168 -
Generalized $\eta$-Ricci solitons on para-Kenmotsu manifolds associated to the Zamkovoy connection
Shahroud azami
Commun. Korean Math. Soc. 2024; 39(1): 175-186
https://doi.org/10.4134/CKMS.c230086 -
The pseudospectra of bounded linear operators on quasi normed space
Aymen ammar, Ameni Bouchekoua, Nawrez Lazrag
Commun. Korean Math. Soc. 2023; 38(3): 773-786
https://doi.org/10.4134/CKMS.c220155 -
Terminal spaces of monoids
Amartya Goswami
Commun. Korean Math. Soc. 2024; 39(1): 259-266
https://doi.org/10.4134/CKMS.c230095
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