Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-10-31
Nonlinear maps preserving the mixed product $_*[X\diamond Y, Z]$ on $*$-algebras
Raof Ahmad Bhat, Abbas Hussain Shikeh, Mohammad Aslam SiddeequeAbstract : 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.
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2023-07-31
On nonnil-SFT rings
Ali Benhissi, Abdelamir DabbabiAbstract : The purpose of this paper is to introduce a new class of rings containing the class of SFT-rings and contained in the class of rings with Noetherian prime spectrum. Let $A$ be a commutative ring with unit and $I$ be an ideal of $A$. We say that $I$ is SFT if there exist an integer $k\geq 1$ and a finitely generated ideal $F\subseteq I$ of $A$ such that $x^k\in F$ for every $x\in I$. The ring $A$ is said to be nonnil-SFT, if each nonnil-ideal (i.e., not contained in the nilradical of $A$) is SFT. We investigate the nonnil-SFT variant of some well known theorems on SFT-rings. Also we study the transfer of this property to Nagata's idealization and the amalgamation algebra along an ideal. Many examples are given. In fact, using the amalgamation construction, we give an infinite family of nonnil-SFT rings which are not SFT.
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2024-04-30
Study of quotient near-rings with additive maps
Abdelkarim Boua, Abderrahmane Raji, Abdelilah ZerbaneAbstract : We consider $\mathcal{N}$ to be a $3$-prime field and $\mathcal{P}$ to be a prime ideal of $\mathcal{N}.$ In this paper, we study the commutativity of the quotient near-ring $\mathcal{N}/\mathcal{P}$ with left multipliers and derivations satisfying certain identities on $P$, generalizing some well-known results in the literature. Furthermore, an example is given to illustrate the necessity of our hypotheses.
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2023-07-31
Fractional integration and differentiation of the $(p,q)$--extended modified Bessel function of the second kind and integral transforms
Purnima Chopra, Mamta Gupta, Kanak ModiAbstract : Our aim is to establish certain image formulas of the $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$ by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$. Corresponding assertions for the Saigo's, 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 $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$ and Fox-Wright function $_{r}\Psi_{s}(z)$.
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2023-10-31
A variant of Wilson's functional equation on semigroups
YOUSSEF ASERRAR, ABDELLATIF CHAHBI, ELHOUCIEN ELQORACHIAbstract : Let $S$ be a semigroup. We determine the complex-valued solutions of the following functional equation \[f(xy)+\mu (y)f(\sigma (y)x) = 2f(x)g(y),\ x,y\in S,\] where $\sigma:S\rightarrow S$ is an automorphism, and $\mu :S\rightarrow \mathbb{C}$ is a multiplicative function such that $\mu (x\sigma (x))=1$ for all $x\in S$.
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2023-07-31
Convergence of sequences in generalized topological spaces via filter
Julio C. Ramos-Fernández, Ennis Rosas, Margot Salas-BrownAbstract : 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.
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2023-10-31
Some classes of operators related to $(m, n)$-paranormal and $(m, n)^*$-paranormal operators
SHINE LAL ENOSE, RAMYA PERUMAL, PRASAD THANKARAJANAbstract : In this paper, we study new classes of operators $k$-quasi $(m, n)$-paranormal operator, $k$-quasi $(m, n)^*$-paranormal operator, $k$-qu\-asi $(m, n)$-class~ $\mathcal{Q}$ operator and $k$-quasi $(m, n)$-class~ $\mathcal{Q^{*}}$ operator which are the generalization of $(m, n)$-paranormal and $(m, n)^*$-paranormal operators. We give matrix characterizations for $k$-quasi $(m, n)$-paranormal and $k$-quasi $(m, n)^*$-paranormal operators. Also we study some properties of $k$-quasi $(m, n)$-class~ $\mathcal{Q}$ operator and $k$-quasi $(m, n)$-class~ $\mathcal{Q}^*$ operators. Moreover, these classes of composition operators on $L^2$ spaces are characterized.
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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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2023-04-30
The measurability of Hewitt-Stromberg measures and dimensions
Zied Douzi, Bilel Selmi, Haythem ZyoudiAbstract : The aim of this paper is to study the descriptive set-theoretic complexity of the Hewitt-Stromberg measure and dimension maps.
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2024-01-31
Conformal Ricci soliton on paracontact metric $(k,\mu)$-manifolds with Schouten-van Kampen connection
PARDIP MANDAL, MOHAMMAD HASAN SHAHID, SARVESH KUMAR YADAVAbstract : The main object of the present paper is to study conformal Ricci soliton on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection. Further, we obtain the result when paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection satisfying the condition $\overset{\star}{C}(\xi,U)\cdot\overset{\star}{S}=0$. Finally we characterized concircular curvature tensor on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection.
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Two linear polynomials shared by an entire function and its linear differential polynomials
Goutam Kumar Ghosh
Commun. Korean Math. Soc. 2023; 38(2): 377-387
https://doi.org/10.4134/CKMS.c210303 -
A study of differential identities on $\sigma$-prime rings
Adnan Abbasi, Md Arshad Madni, Muzibur Rahman Mozumder
Commun. Korean Math. Soc. 2023; 38(3): 679-693
https://doi.org/10.4134/CKMS.c220240 -
S-coherent property in trivial extension and in amalgamated duplication
MOHAMED CHHITI, SALAH EDDINE MAHDOU
Commun. Korean Math. Soc. 2023; 38(3): 705-714
https://doi.org/10.4134/CKMS.c220260 -
Equality in degrees of compactness: Schauder's theorem and $s$-numbers
Asuman Guven Aksoy, Daniel Akech Thiong
Commun. Korean Math. Soc. 2023; 38(4): 1127-1139
https://doi.org/10.4134/CKMS.c230003
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Uniform distributions on curves and quantization
Joseph Rosenblatt, Mrinal Kanti Roychowdhury
Commun. Korean Math. Soc. 2023; 38(2): 431-450
https://doi.org/10.4134/CKMS.c210434 -
Nonnil-$S$-coherent rings
Najib Mahdou, El Houssaine Oubouhou
Commun. Korean Math. Soc. 2024; 39(1): 45-58
https://doi.org/10.4134/CKMS.c230065 -
Transversal lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds
Shiv Sharma Shukla, Vipul Singh
Commun. Korean Math. Soc. 2023; 38(4): 1191-1213
https://doi.org/10.4134/CKMS.c220309 -
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
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