Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
Most Read
HOME
VIEW ARTICLES
Most Read
VIEW ARTICLES
Most Read
-
2023-09-01
Topologically stable points and uniform limits
Namjip Koo, Hyunhee LeeAbstract : In this paper we study a pointwise version of Walters topological stability in the class of homeomorphisms on a compact metric space. We also show that if a sequence of homeomorphisms on a compact metric space is uniformly expansive with the uniform shadowing property, then the limit is expansive with the shadowing property and so topologically stable. Furthermore, we give examples to illustrate our results.
-
2023-03-01
On $S$-multiplication rings
Mohamed Chhiti, Soibri MoindzeAbstract : Let $R$ be a commutative ring with identity and $S$ be a multiplicatively closed subset of $R$. In this article we introduce a new class of ring, called $S$-multiplication rings which are $S$-versions of multiplication rings. An $R$-module $M$ is said to be $S$-multiplication if for each submodule $N$ of $M$, $sN\subseteq JM\subseteq N$ for some $s\in S$ and ideal $J$ of $R$ (see for instance [4, Definition 1]). An ideal $I$ of $R$ is called $S$-multiplication if $I$ is an $S$-multiplication $R$-module. A commutative ring $R$ is called an $S$-multiplication ring if each ideal of $R$ is $S$-multiplication. We characterize some special rings such as multiplication rings, almost multiplication rings, arithmetical ring, and $S$-$PIR$. Moreover, we generalize some properties of multiplication rings to $S$-multiplication rings and we study the transfer of this notion to various context of commutative ring extensions such as trivial ring extensions and amalgamated algebras along an ideal.
-
2022-05-01
The ideal class group of polynomial overrings of the ring of integers
Gyu Whan ChangAbstract : Let $D$ be an integral domain with quotient field $K$, $Pic(D)$ be the ideal class group of $D$, and $X$ be an indeterminate. A polynomial overring of $D$ means a subring of $K[X]$ containing $D[X]$. In this paper, we study almost Dedekind domains which are polynomial overrings of a principal ideal domain $D$, defined by the intersection of $K[X]$ and rank-one discrete valuation rings with quotient field $K(X)$, and their ideal class groups. Next, let $\mathbb{Z}$ be the ring of integers, $\mathbb{Q}$ be the field of rational numbers, and $\mathfrak{G}_f$ be the set of finitely generated abelian groups (up to isomorphism). As an application, among other things, we show that there exists an overring $R$ of $\mathbb{Z}[X]$ such that (i) $R$ is a Bezout domain, (ii) $R \cap \mathbb{Q}[X]$ is an almost Dedekind domain, (iii) $Pic(R \cap \mathbb{Q}[X]) = \bigoplus_{G \in \mathfrak{G}_f}G$, (iv) for each $G \in \mathfrak{G}_f$, there is a multiplicative subset $S$ of $\mathbb{Z}$ such that $R_S \cap \mathbb{Q}[X]$ is a Dedekind domain with $Pic(R_S \cap \mathbb{Q}[X]) = G$, and (v) every invertible integral ideal $I$ of $R \cap \mathbb{Q}[X]$ can be written uniquely as $I = X^nQ_1^{e_1} \cdots Q_k^{e_k}$ for some integer $n \geq 0$, maximal ideals $Q_i$ of $R \cap \mathbb{Q}[X]$, and integers $e_i \neq 0$. We also completely characterize the almost Dedekind polynomial overrings of $\mathbb{Z}$ containing Int$(\mathbb{Z})$.
-
2023-03-01
Ricci-Bourguignon solitons and Fischer-Marsden conjecture on generalized Sasakian-space-forms with $\beta$-Kenmotsu structure
Sudhakar Kumar Chaubey, Young Jin SuhAbstract : Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with $\beta$-Kenmotsu structure. It is proven that a $(2n+1)$-dimensional generalized Sasakian-space-form with $\beta$-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with $\beta$-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either $\Psi \backslash T^{k} \times M^{2n+1-k}$ or gradient $\eta$-Yamabe soliton.
-
2022-09-01
Weakly equivariant classification of small covers over a product of simplicies
Aslı Güçlükan İlhan, Sabri Kaan Gürbüzer
Abstract : Given a dimension function $\omega$, we introduce the notion of an $\omega$-vector weighted digraph and an $\omega$-equivalence between them. Then we establish a bijection between the weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over a product of simplices $\Delta^{\omega(1)}\times\cdots \times \Delta^{\omega(m)}$ and the set of $\omega$-equivalence classes of $\omega$-vector weighted digraphs with $m$-labeled vertices, where $n$ is the sum of the dimensions of the simplicies. Using this bijection, we obtain a formula for the number of weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over a product of three simplices.
-
2023-03-01
Prime factorization of ideals in commutative rings, with a focus on Krull rings
Gyu Whan Chang, Jun Seok OhAbstract : Let $R$ be a commutative ring with identity. The structure theorem says that $R$ is a PIR (resp., UFR, general ZPI-ring, $\pi$-ring) if and only if $R$ is a finite direct product of PIDs (resp., UFDs, Dedekind domains, $\pi$-domains) and special primary rings. All of these four types of integral domains are Krull domains, so motivated by the structure theorem, we study the prime factorization of ideals in a ring that is a finite direct product of Krull domains and special primary rings. Such a ring will be called a general Krull ring. It is known that Krull domains can be characterized by the star operations $v$ or $t$ as follows: An integral domain $R$ is a Krull domain if and only if every nonzero proper principal ideal of $R$ can be written as a finite $v$- or $t$-product of prime ideals. However, this is not true for general Krull rings. In this paper, we introduce a new star operation $u$ on $R$, so that $R$ is a general Krull ring if and only if every proper principal ideal of $R$ can be written as a finite $u$-product of prime ideals. We also study several ring-theoretic properties of general Krull rings including Kaplansky-type theorem, Mori-Nagata theorem, Nagata rings, and Noetherian property.
-
2022-07-01
Uniqueness of quasi-roots in right-angled Artin groups
Eon-Kyung Lee, Sang-Jin LeeAbstract : We introduce the notion of quasi-roots and study their uniqueness in right-angled Artin groups.
-
2023-07-01
Construction of a Mattila--Sj\"{o}lin type function over a finite field
Daewoong Cheong, Jinbeom KimAbstract : Let $\mathbb F_q$ be a finite field with $q$ elements. A function $f: \mathbb F_q^d\times \mathbb F_q^d \to \mathbb F_q$ is called a Mattila--Sj\"{o}lin type function of index $\gamma \in \mathbb R$ if $\gamma$ is the smallest real number such that whenever $|E|\geq Cq^{\gamma}$ for a sufficiently large constant $C$, the set $f(E,E):=\{f(x,y): x, y\in E\}$ is equal to $\mathbb F_q$. In this article, we construct an example of a Mattila--Sj\"{o}lin type function $f$ and provide its index, generalizing the result of Cheong, Koh, Pham and Shen [1].
-
2022-07-01
On $3^k$-regular cubic partitions
Nayandeep Deka Baruah, Hirakjyoti DasAbstract : Recently, Gireesh, Shivashankar, and Naika [11] found some infinite classes of congruences for the 3- and the 9-regular cubic partitions modulo powers of 3. We extend their study to all the $3^k$-regular cubic partitions. We also find new families of congruences.
-
2022-05-01
On weighted compactness of commutators of bilinear fractional maximal operator
Qianjun He, Juan ZhangAbstract : Let $\mathcal{M}_{\alpha}$ be a bilinear fractional maximal operator and $BM_{\alpha}$ be a fractional maximal operator associated with the bilinear Hilbert transform. In this paper, the compactness on weighted Lebesgue spaces are considered for commutators of bilinear fractional maximal operators; these commutators include the fractional maximal linear commutators $\mathcal{M}_{\alpha,b}^{j}$ and $BM_{\alpha, b}^{j} $ $(j=1,2)$, the fractional maximal iterated commutator $\mathcal{M}_{\alpha,\vec{b}}$, and $BM_{\alpha, \vec{b}}$, where $b\in{\rm BMO}(\mathbb{R}^{d})$ and $\vec{b}=(b_{1},b_{2})\in{\rm BMO}(\mathbb{R}^{d})\times {\rm BMO}(\mathbb{R}^{d})$. In particular, we improve the well-known results to a larger scale for $1/2
Most Read
-
Schur convexity of $L$-conjugate means and its applications
Chun-Ru Fu
, Huan-Nan Shi, Dong-Sheng WangJ. Korean Math. Soc. 2023; 60(3): 503-520
https://doi.org/10.4134/JKMS.j220039 -
Sharp Ore-type conditions for the existence of an even $[4,b]$-factor in a graph
Eun-Kyung Cho, Su-Ah Kwon, Suil O
J. Korean Math. Soc. 2022; 59(4): 757-774
https://doi.org/10.4134/JKMS.j210605 -
Weak Herz-type Hardy spaces with variable exponents and applications
Souad Ben Seghier
J. Korean Math. Soc. 2023; 60(1): 33-69
https://doi.org/10.4134/JKMS.j210764 -
Birkhoff's ergodic theorems in terms of weighted inductive means
Byoung Jin Choi, Jae Hun Kim
J. Korean Math. Soc. 2022; 59(3): 549-570
https://doi.org/10.4134/JKMS.j210239
Most Downloaded
-
Thomas algorithms for systems of fourth-order finite difference methods
Soyoon Bak, Philsu Kim, Sangbeom Park
J. Korean Math. Soc. 2022; 59(5): 891-909
https://doi.org/10.4134/JKMS.j210701 -
The Bongartz's theorem of Gorenstein cosilting complexes
Hailou Yao, Qianqian Yuan
J. Korean Math. Soc. 2023; 60(6): 1337-1364
https://doi.org/10.4134/JKMS.j230208 -
Schur convexity of $L$-conjugate means and its applications
Chun-Ru Fu
, Huan-Nan Shi, Dong-Sheng WangJ. Korean Math. Soc. 2023; 60(3): 503-520
https://doi.org/10.4134/JKMS.j220039 -
Low rank orthogonal bundles and quadric fibrations
Insong Choe, George H. Hitching
J. Korean Math. Soc. 2023; 60(6): 1137-1169
https://doi.org/10.4134/JKMS.j220125
Editorial Office
✕
JKMS
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd