Abstract : In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.
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.
Abstract : In the paper, we have exhaustively studied about the uniqueness of meromorphic function sharing two small functions with its $k$-th derivative as these types of results have never been studied earlier. We have obtained a series of results which will improve and extend some recent results of Banerjee-Maity \cite{Ban-Maity_Contemp.}.
Abstract : In this paper, we study para-Kenmotsu manifolds admitting generalized $\eta$-Ricci solitons associated to the Zamkovoy connection. We provide an example of generalized $\eta$-Ricci soliton on a para-Kenmotsu manifold to prove our results.
Abstract : In this paper, we introduce the pseudospectra of bounded linear operators on quasi normed space and study its proprieties. Beside that, we establish the relationship between the pseudospectra of a sequence of bounded linear operators and its limit.
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.
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.
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.
Abstract : 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 $\kappa < 0$.
Abstract : We give a characterization of zero divisors of the ring $C[a,b]$. Using the Weierstrass approximation theorem, we completely characterize topological divisors of zero of the Banach algebra $C[a,b]$. We also characterize the zero divisors and topological divisors of zero in $\ell^\infty$. Further, we show that zero is the only zero divisor in the disk algebra $\mathscr{A}(\mathbb{D})$ and that the class of singular elements in $\mathscr{A}(\mathbb{D})$ properly contains the class of topological divisors of zero. Lastly, we construct a class of topological divisors of zero of $\mathscr{A}(\mathbb{D})$ which are not zero divisors.
Serap Bulut
Commun. Korean Math. Soc. 2022; 37(3): 723-734
https://doi.org/10.4134/CKMS.c210196
Abdellah Mamouni, Lahcen Oukhtite, Mohammed Zerra
Commun. Korean Math. Soc. 2023; 38(1): 79-87
https://doi.org/10.4134/CKMS.c220004
Abasalt Bodaghi, Hassan Feizabadi
Commun. Korean Math. Soc. 2022; 37(3): 801-812
https://doi.org/10.4134/CKMS.c210300
Junghyun Hong, Jongmin Lee, Ho Park
Commun. Korean Math. Soc. 2023; 38(1): 89-96
https://doi.org/10.4134/CKMS.c220015
soufiane Benkouider, Abita Rahmoune
Commun. Korean Math. Soc. 2023; 38(3): 943-966
https://doi.org/10.4134/CKMS.c220225
YOUSSEF ASERRAR, ABDELLATIF CHAHBI, ELHOUCIEN ELQORACHI
Commun. Korean Math. Soc. 2023; 38(4): 1063-1074
https://doi.org/10.4134/CKMS.c220315
Bouthaina Abdelhedi, Wissal Boubaker, Nedra Moalla
Commun. Korean Math. Soc. 2023; 38(4): 1029-1044
https://doi.org/10.4134/CKMS.c220019
SeokJun Hong, SiHyun Moon, Ho Park, SeoYeon Park, SoYoung Seo
Commun. Korean Math. Soc. 2023; 38(3): 695-704
https://doi.org/10.4134/CKMS.c220245
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