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.
Abstract : Let $ G_{k,n}(\h) $ for $ 2\leq k
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 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}.
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.
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.
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 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.
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.
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.
B\"{u}lent Nafi \"{O}rnek
Commun. Korean Math. Soc. 2023; 38(2): 389-400
https://doi.org/10.4134/CKMS.c210315
Gemechis File Duressa, Tariku Birabasa Mekonnen
Commun. Korean Math. Soc. 2023; 38(1): 299-318
https://doi.org/10.4134/CKMS.c220020
Shaymaa S. Essa, Husam Q. Mohammad
Commun. Korean Math. Soc. 2023; 38(1): 55-67
https://doi.org/10.4134/CKMS.c210427
S. Joe Christin Mary, Ayyadurai Tamilselvan
Commun. Korean Math. Soc. 2023; 38(1): 281-298
https://doi.org/10.4134/CKMS.c210252
M. Alimohammady, A. Rezvani, C. Tunc
Commun. Korean Math. Soc. 2023; 38(4): 1045-1061
https://doi.org/10.4134/CKMS.c220308
Asuman Guven Aksoy, Daniel Akech Thiong
Commun. Korean Math. Soc. 2023; 38(4): 1127-1139
https://doi.org/10.4134/CKMS.c230003
Anass Assarrar, Najib Mahdou
Commun. Korean Math. Soc. 2023; 38(4): 1001-1017
https://doi.org/10.4134/CKMS.c230004
Ponmana Selvan Arumugam, Ganapathy Gandhi, Saravanan Murugesan, Veerasivaji Ramachandran
Commun. Korean Math. Soc. 2023; 38(4): 1163-1173
https://doi.org/10.4134/CKMS.c230034
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