Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2022-07-31
Positive solution and ground state solution for a Kirchhoff type equation with critical growth
Caixia Chen, Aixia QianAbstract : In this paper, we consider the following Kirchhoff type equation on the whole space $$\left\{\aligned &-(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}dx)\triangle u = u^{5} + \lambda k(x)g(u), \ x\in \mathbb{R}^{3},\\ & u\in\mathcal{D}^{1,2}(\mathbb{R}^{3}),\endaligned\right.$$ where $\lambda>0$ is a real number and $k, g$ satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.
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2024-01-31
Depth and Stanley depth of two special classes of monomial ideals
Xiaoqi WeiAbstract : In this paper, we define two new classes of monomial ideals $I_{l,d}$ and $J_{k,d}$. When $d\geq 2k+1$ and $l\leq d-k-1$, we give the exact formulas to compute the depth and Stanley depth of quotient rings $S/I_{l,d}^{t}$ for all $t\geq 1$. When $d=2k=2l$, we compute the depth and Stanley depth of quotient ring $S/I_{l,d}$. When $d\geq 2k$, we also compute the depth and Stanley depth of quotient ring $S/J_{k,d}$.
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2022-07-31
On right regularity of commutators
Da Woon Jung, Chang Ik Lee, Yang Lee, Sangwon Park, Sung Ju Ryu, Hyo Jin SungAbstract : We study the structure of right regular commutators, and call a ring $R$ {\it strongly $C$-regular} if $ab-ba\in (ab-ba)^2R$ for any $a, b\in R$. We first prove that a noncommutative strongly $C$-regular domain is a division algebra generated by all commutators; and that a ring (possibly without identity) is strongly $C$-regular if and only if it is Abelian $C$-regular (from which we infer that strong $C$-regularity is left-right symmetric). It is proved that for a strongly $C$-regular ring $R$, (i) if $R/W(R)$ is commutative, then $R$ is commutative; and (ii) every prime factor ring of $R$ is either a commutative domain or a noncommutative division ring, where $W(R)$ is the Wedderburn radical of $R$.
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2022-09-30
N-pure ideals and mid rings
Mohsen AghajaniAbstract : In this paper, we introduce the concept of N-pure ideal as a generalization of pure ideal. Using this concept, a new and interesting type of rings is presented, we call it a mid ring. Also, we provide new characterizations for von Neumann regular and zero-dimensional rings. Moreover, some results about mp-ring are given. Finally, a characterization for mid rings is provided. Then it is shown that the class of mid rings is strictly between the class of reduced mp-rings (p.f.~rings) and the class of mp-rings.
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2022-11-30
An associated sequence of ideals of an increasing sequence of rings
Ali Benhissi, Abdelamir DabbabiAbstract : Let ${\mathcal A}=(A_n)_{n\geq 0}$ be an increasing sequence of rings. We say that ${\mathcal I}=(I_n)_{n\geq 0}$ is an associated sequence of ideals of ${\mathcal A}$ if $I_0=A_0$ and for each $n\geq 1$, $I_n$ is an ideal of $A_n$ contained in $I_{n+1}$. We define the polynomial ring and the power series ring as follows: ${\mathcal I}[X]=\lbrace f={\sum_{i=0}^n}a_iX^i\in {\mathcal A}[X]: n\in \mathbb{N}, a_i\in I_i\rbrace$ and ${\mathcal I}[[X]]=\lbrace f={\sum_{i=0}^{+\infty}}a_iX^i\in {\mathcal A}[[X]]: a_i\in I_i\rbrace$. In this paper we study the Noetherian and the SFT properties of these rings and their consequences.
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2022-07-31
Uniqueness of meromorphic solutions of a certain type of difference equations
Jun-Fan Chen, Shu-Qing LinAbstract : In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions $f(z)$ and $g(z)$ of the following complex difference equation $$A_{1}(z)f(z+1)+A_{0}(z)f(z)=F(z)e^{\alpha(z)}$$ when they share 0, $\infty$ CM, where $A_{1}(z),$ $A_{0}(z),$ $F(z)$ are non-zero polynomials, $\alpha(z)$ is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.
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2022-05-31
Characterizing $S$-flat modules and $S$-von Neumann regular rings by uniformity
Xiaolei ZhangAbstract : Let $R$ be a ring and $S$ a multiplicative subset of $R$. An $R$-module $T$ is called $u$-$S$-torsion ($u$-always abbreviates uniformly) provided that $sT=0$ for some $s\in S$. The notion of $u$-$S$-exact sequences is also introduced from the viewpoint of uniformity. An $R$-module $F$ is called $u$-$S$-flat provided that the induced sequence $0\rightarrow A\otimes_RF\rightarrow B\otimes_RF\rightarrow C\otimes_RF\rightarrow 0$ is $u$-$S$-exact for any $u$-$S$-exact sequence $0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0$. A ring $R$ is called $u$-$S$-von Neumann regular provided there exists an element $s\in S$ satisfying that for any $a\in R$ there exists $r\in R$ such that $sa=ra^2$. We obtain that a ring $R$ is a $u$-$S$-von Neumann regular ring if and only if any $R$-module is $u$-$S$-flat. Several properties of $u$-$S$-flat modules and $u$-$S$-von Neumann regular rings are obtained.
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2022-05-31
Strong classification of extensions of classifiable $C^{*}$-algebras
S{\o}ren Eilers, Gunnar Restorff, Efren RuizAbstract : We show that certain extensions of classifiable $C^{*}$-algebras are strongly classified by the associated six-term exact sequence in $K$-theory together with the positive cone of $K_{0}$-groups of the ideal and quotient. We use our results to completely classify all unital graph $C^{*}$-algebras with exactly one non-trivial ideal.
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2023-01-31
On the top local cohomology and formal local cohomology modules
Shahram Rezaei, Behrouz SadeghiAbstract : Let ${\mathfrak{a}}$ and $\mathfrak{b}$ be ideals of a commutative Noetherian ring $R$ and $M$ a finitely generated $R$-module of finite dimension $d>0$. In this paper, we obtain some results about the annihilators and attached primes of top local cohomology and top formal local cohomology modules. In particular, we determine $\operatorname{Ann} (\mathfrak{b}\operatorname{H}_{\mathfrak{a}}^{d}(M))$, $\operatorname{Att} (\mathfrak{b}\operatorname{H}_{\mathfrak{a}}^{d}(M))$, $\operatorname{Ann}(\mathfrak{b}\mathfrak{F}_{\mathfrak{a}}^{d} (M))$ and $\operatorname{Att} (\mathfrak{b}\mathfrak{F}_{\mathfrak{a}}^{d} (M))$.
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2024-01-31
A cotorsion pair induced by the class of Gorenstein $(m,n)$-flat modules
Qiang YangAbstract : In this paper, we introduce the notion of Gorenstein $(m,n)$-flat modules as an extension of $(m,n)$-flat left $R$-modules over a ring $R$, where $m$ and $n$ are two fixed positive integers. We demonstrate that the class of all Gorenstein $(m,n)$-flat modules forms a Kaplansky class and establish that ($\mathcal{GF}_{m,n}(R)$,$\mathcal{GC}_{m,n}(R)$) constitutes a hereditary perfect cotorsion pair (where $\mathcal{GF}_{m,n}(R)$ denotes the class of Gorenstein $(m,n)$-flat modules and $\mathcal{GC}_{m,n}(R)$ refers to the class of Gorenstein $(m,n)$-cotorsion modules) over slightly $(m,n)$-coherent rings.
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Characterizing $S$-flat modules and $S$-von Neumann regular rings by uniformity
Xiaolei Zhang
Bull. Korean Math. Soc. 2022; 59(3): 643-657
https://doi.org/10.4134/BKMS.b210291 -
Dynamics of random dynamical systems
Enkhbayar Azjargal, Zorigt Choinkhor, Nyamdavaa Tsegmid
Bull. Korean Math. Soc. 2023; 60(4): 1131-1139
https://doi.org/10.4134/BKMS.b220595 -
Lens spaces admitting minimal symplectic fillings with the second Betti number one
Heesang Park, Dongsoo Shin
Bull. Korean Math. Soc. 2023; 60(1): 113-122
https://doi.org/10.4134/BKMS.b210923 -
Dually flat and projectively flat Finsler warped product structures
Xiaoling Zhang, Xuesong Zhang, Lili Zhao
Bull. Korean Math. Soc. 2022; 59(6): 1359-1370
https://doi.org/10.4134/BKMS.b210760
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Bredon homology of wallpaper groups
Ramon Flores
Bull. Korean Math. Soc. 2023; 60(6): 1497-1522
https://doi.org/10.4134/BKMS.b220669 -
On the construction of optimal linear codes of dimension four
ATSUYA KATO, TATSUYA MARUTA, KEITA NOMURA
Bull. Korean Math. Soc. 2023; 60(5): 1237-1252
https://doi.org/10.4134/BKMS.b220613 -
Anti-flips of the blow-ups of the projective spaces at torus invariant points
Hiroshi Sato, Shigehito Tsuzuki
Bull. Korean Math. Soc. 2023; 60(6): 1705-1714
https://doi.org/10.4134/BKMS.b220864 -
Second main theorem for meromorphic mappings on $p$-parabolic manifolds intersecting hypersurfaces in subgeneral position
Yuehuan Zhu
Bull. Korean Math. Soc. 2023; 60(6): 1621-1639
https://doi.org/10.4134/BKMS.b220769
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