Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2024-01-31
Skew brace enhancements and virtual links
Melody Chang, Sam NelsonAbstract : We use the structure of skew braces to enhance the biquandle counting invariant for virtual knots and links for finite biquandles defined from skew braces. We introduce two new invariants: a single-variable polynomial using skew brace ideals and a two-variable polynomial using the skew brace group structures. We provide examples to show that the new invariants are not determined by the counting invariant and hence are proper enhancements.
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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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2024-04-30
Cohen-Macaulay dimension for complexes
Fatemeh Mohammadi Aghjeh MashhadAbstract : In this paper, our focus lies in exploring the concept of Cohen-Macaulay dimension within the category of homologically finite complexes. We prove that over a local ring $(R,\fm)$, any homologically finite complex $X$ with a finite Cohen-Macaulay dimension possesses a finite \emph{$CM$-resolution}. This means that there exists a bounded complex $G$ of finitely generated $R$-modules, such that $G$ is isomorphic to $X$ and each nonzero $G_i$ within the complex $G$ has zero Cohen-Macaulay dimension.
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2024-04-30
A generalization of the symmetry property of a ring via its endomorphism
Fatma Kaynarca
, H. Melis Tekin Akcin Abstract : Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly $\alpha$-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring $R$ as strongly $\alpha$-symmetric if the skew polynomial ring $R[x;\alpha]$ is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly $\alpha$-symmetric rings.
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2024-04-30
Invariant null rigged hypersurfaces of indefinite nearly ${\alpha}$-Sasakian manifolds
Mohamed H. A. Hamed, Fortune MassambaAbstract : We introduce invariant rigged null hypersurfaces of indefinite almost contact manifolds, by paying attention to those of indefinite nearly $\alpha$-Sasakian manifolds. We prove that, under some conditions, there exist leaves of the integrable screen distribution of the ambient manifolds admitting nearly $\alpha$-Sasakian structures.
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2024-04-30
Parallel shrinking projection method for fixed point and generalized equilibrium problems on Hadamard manifold
HAMMED ANUOLUWAPO ABASS, KAZEEM OLAWALE OYEWOLEAbstract : In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.
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2024-04-30
On the number of equivalence classes of bi-partitions arising from the color change
Byungchan KimAbstract : We introduce a new class of bi-partition function $c_k(n)$, which counts the number of bi-color partitions of $n$ in which the second color only appears at the parts that are multiples of $k$. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo $k$. We show that the generating function for $c_k(n)$ involves the partial theta function and obtain the following congruences: \begin{align*} c_2 (27n+26) &\equiv 0 \pmod{3} \\ \intertext{and} c_3 (4n + 2 ) &\equiv 0 \pmod{2}. \end{align*}
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2024-04-30
On the convergence of Ishikawa iteration with errors for real continuous functions
Kittithat Boonpot, Satit SaejungAbstract : We point out an error appeared in the paper of Yuan et al.~\cite{YCQ} and present a correction of their result under a more general assumption. Moreover, we discuss the validity of the conditions imposed on the sequences of error terms.
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2024-04-30
When every finitely generated regular ideal is finitely presented
MOHAMED CHHITI, SALAH EDDINE MAHDOUAbstract : In this paper, we introduce a weak version of coherent that we call regular coherent property. A ring is called regular coherent, if every finitely generated regular ideal is finitely presented. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.
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2024-04-30
Nonlinear mixed $\ast$-Jordan type $n$-derivations on $\ast$-algebras
Raof Ahmad Bhat, Abbas Hussain Shikeh, Mohammad Aslam SiddeequeAbstract : Let $ \mathfrak{R}$ be a $\ast$-algebra with unity $I$ and a nontrivial projection $P_1$. In this paper, we show that under certain restrictions if a map $ \Psi : \mathfrak{R} \to \mathfrak{R}$ satisfies \begin{align*} &\ \Psi ( S_1 \diamond S_2 \diamond \cdots \diamond S_{n-1} \bullet S_n) \\ =&\ \sum_{k = 1}^{n} S_1 \diamond S_2 \diamond \cdots \diamond S_{k-1} \diamond \Psi( S_k)\diamond S_{k+1} \diamond \cdots \diamond S_{n-1} \bullet S_n \end{align*} for all $ S_{n-2}, S_{n-1}, S_n \in \mathfrak{R} $ and $S_i=I$ for all $i \in \{1,2,\hdots, n-3\}$, where $n\geq 3$, then $ \Psi$ is an additive $\ast$-derivation.
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Certain study of generalized $B$ curvature tensor within the framework of Kenmotsu manifold
Rahuthanahalli Thimmegowda Naveen Kumar, Basavaraju Phalaksha Murthy, Puttasiddappa Somashekhara, Venkatesha Venkatesha
Commun. Korean Math. Soc. 2023; 38(3): 893-900
https://doi.org/10.4134/CKMS.c220287 -
New volume comparison with almost Ricci soliton
Shahroud azami, Sakineh Hajiaghasi
Commun. Korean Math. Soc. 2022; 37(3): 839-849
https://doi.org/10.4134/CKMS.c210097 -
Quantization for a probability distribution generated by an infinite iterated function system
Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury
Commun. Korean Math. Soc. 2022; 37(3): 765-800
https://doi.org/10.4134/CKMS.c210266 -
The $u$-$S$-weak global dimensions of commutative rings
Xiaolei Zhang
Commun. Korean Math. Soc. 2023; 38(1): 97-112
https://doi.org/10.4134/CKMS.c220016
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Space of homeomorphisms under regular topology
Mir Aaliya, Sanjay Mishra
Commun. Korean Math. Soc. 2023; 38(4): 1299-1307
https://doi.org/10.4134/CKMS.c220349 -
Existence theorems for critical degenerate equations involving the Grushin operators
Huong Thi Thu Nguyen, Tri Minh Nguyen
Commun. Korean Math. Soc. 2023; 38(1): 137-151
https://doi.org/10.4134/CKMS.c220030 -
On the generalized Ornstein-Uhlenbeck operators with regular and singular potentials in weighted $L^{p}$-spaces
Imen Metoui
Commun. Korean Math. Soc. 2024; 39(1): 149-160
https://doi.org/10.4134/CKMS.c230133 -
Some results on the geometry of a non-conformal deformation of a metric
Nour Elhouda Djaa, Abderrahim Zagane
Commun. Korean Math. Soc. 2022; 37(3): 865-879
https://doi.org/10.4134/CKMS.c210207
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