Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2024-03-31
Some factorization properties of idealization in commutative rings with zero divisors
Sina Eftekhari, Sayyed Heidar Jafari, Mahdi Reza KhorsandiAbstract : We study some factorization properties of the idealization $R$(+)$M$ of a module $M$ in a commutative ring $R$ which is not necessarily a domain. We show that $R$(+)$M$ is ACCP if and only if $R$ is ACCP and $M$ satisfies ACC on its cyclic submodules. We give an example to show that the BF property is not necessarily preserved in idealization, and give some conditions under which $R$(+)$M$ is a BFR. We also characterize the idealization rings which are UFRs.
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2023-03-31
Uniqueness results on meromorphic functions and their difference operators sharing targets with weight
Thu Thuy Hoang, Hong Nhat Nguyen, Duc Thoan PhamAbstract : Let $f$ be a nonconstant meromorphic function of hyper-order strictly less than 1, and let $c\in\mathbb C\setminus\{0\}$ such that $f(z + c) \not\equiv f(z)$. We prove that if $f$ and its exact difference $\Delta_cf(z) = f(z + c) - f(z)$ share partially $0, \infty$ CM and share 1 IM, then $\Delta_cf = f$, where all 1-points with multiplicities more than 2 do not need to be counted. Some similar uniqueness results for such meromorphic functions partially sharing targets with weight and their shifts are also given. Our results generalize and improve the recent important results.
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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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2023-03-31
On meromorphic solutions of nonlinear partial differential-difference equations of first order in several complex variables
Qibin Cheng, Yezhou Li, Zhixue LiuAbstract : This paper is concerned with the value distribution for meromorphic solutions $f$ of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions $f$ are uniquely determined by the poles of $f$ and the zeros of $f-c, f-d$ (counting multiplicities) for two distinct small functions $c, d$.
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2023-05-31
Compact composition operators on Besov spaces on the unit ball
Chao ZhangAbstract : In this paper, we give new necessary and sufficient conditions for the compactness of composition operator on the Besov space and the Bloch space of the unit ball, which, to a certain extent, generalizes the results given by M. Tjani in [10].
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2023-03-31
Primary decomposition of submodules of a free module of finite rank over a B\'ezout domain
Fatemeh Mirzaei, Reza NekooeiAbstract : Let $R$ be a commutative ring with identity. In this paper, we characterize the prime submodules of a free $R$-module $F$ of finite rank with at most $n$ generators, when $R$ is a $\text{GCD}$ domain. Also, we show that if $R$ is a B\'ezout domain, then every prime submodule with $n$ generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of $F$ over a B\'ezout domain and characterize the minimal primary decomposition of this submodule.
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2024-03-31
Certain differential identities in prime rings with anti-automorphisms
Abbas Hussain Shikeh, Mohammad Aslam SiddeequeAbstract : The objective of this paper is to study some central identities involving generalized derivations and anti-automorphisms in prime rings. Using the tools of the theory of functional identities, several known results have been generalized as well as improved.
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2024-03-31
Using rotationally symmetric planes to establish topological finiteness of manifolds
Eric ChoiAbstract : Let $(M, p)$ denote a noncompact manifold $M$ together with arbitrary basepoint $p$. In \cite{KonTan-II}, Kondo-Tanaka show that $(M, p)$ can be compared with a rotationally symmetric plane $M_m$ in such a way that if $M_m$ satisfies certain conditions, then $M$ is proved to be topologically finite. We substitute Kondo-Tanaka's condition of finite total curvature of $M_m$ with a weaker condition and show that the same conclusion can be drawn. We also use our results to show that when $M_m$ satisfies certain conditions, then $M$ is homeomorphic to $\mathbb{R}^n$.
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2023-09-30
Differences of weighted composition operators on Bergman spaces induced by doubling weights
Jiale ChenAbstract : We characterize the boundedness and compactness of differences of weighted composition operators acting from weighted Bergman spaces $A^p_{\omega}$ to Lebesgue spaces $L^q(d\mu)$ for all $0<p,q<\infty$, where $\omega$ is a radial weight on the unit disk admitting a two-sided doubling condition.
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2023-03-31
On reversible $\mathbb{Z}_2$-double cyclic codes
Nupur PatankerAbstract : A binary linear code is said to be a $\mathbb{Z}_2$-double cyclic code if its coordinates can be partitioned into two subsets such that any simultaneous cyclic shift of the coordinates of the subsets leaves the code invariant. These codes were introduced in [6]. A $\mathbb{Z}_2$-double cyclic code is called reversible if reversing the order of the coordinates of the two subsets leaves the code invariant. In this note, we give necessary and sufficient conditions for a $\mathbb{Z}_2$-double cyclic code to be reversible. We also give a relation between reversible $\mathbb{Z}_2$-double cyclic code and LCD $\mathbb{Z}_2$-double cyclic code for the separable case and we present a few examples to show that such a relation doesn't hold in the non-separable case. Furthermore, we list examples of reversible $\mathbb{Z}_2$-double cyclic codes of length $\leq 10$.
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On the structure of certain subset of Farey sequence
Xing-Wang Jiang, Ya-Li Li
Bull. Korean Math. Soc. 2023; 60(4): 915-931
https://doi.org/10.4134/BKMS.b220396 -
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 -
On a generalization of unit regular rings
Tahire Ozen
Bull. Korean Math. Soc. 2023; 60(6): 1463-1475
https://doi.org/10.4134/BKMS.b220573 -
Zero sums of dual Toeplitz products on the orthogonal complement of the Dirichlet space
Young Joo Lee
Bull. Korean Math. Soc. 2023; 60(1): 161-170
https://doi.org/10.4134/BKMS.b220042
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Fixed-width partitions according to the parity of the even parts
John Maxwell Campbell
Bull. Korean Math. Soc. 2023; 60(4): 1017-1024
https://doi.org/10.4134/BKMS.b220457 -
A model of retirement and consumption-portfolio choice
Junkee Jeon, Hyeng Keun Koo
Bull. Korean Math. Soc. 2023; 60(4): 1101-1129
https://doi.org/10.4134/BKMS.b220553 -
Structure of idempotents in polynomial rings and matrix rings
Juan Huang, Tai Keun Kwak, Yang Lee, Zhelin Piao
Bull. Korean Math. Soc. 2023; 60(5): 1321-1334
https://doi.org/10.4134/BKMS.b220692 -
Relationship between the structure of a factor ring $R/P$ and derivations of $R$
Karim Bouchannafa, Moulay Abdallah Idrissi, Lahcen Oukhtite
Bull. Korean Math. Soc. 2023; 60(5): 1281-1293
https://doi.org/10.4134/BKMS.b220654
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