Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-01-31
Bisectors in the Heisenberg group I
Gaoshun Gou, Yueping Jiang, Ioannis D. PlatisAbstract : We show that metric bisectors with respect to the Kor\'anyi metric in the Heisenberg group are spinal spheres and vice versa. We also calculate explicitly their horizontal mean curvature.
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2023-07-31
Annihilator ideals of simple modules of restricted quantized enveloping algebra
Yu WangAbstract : Let $U$ be the restricted quantized enveloping algebra $\widetilde{U}_q(\mathfrak{sl}_2)$ over an algebraically closed field of characteristic zero, where $q$ is a primitive $l$-th root of unity (with $l$ being odd and greater than $1$). In this paper we show that any indecomposable submodule of $U$ under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of $U$. Moreover, we classify annihilator ideals of simple modules of $U$ by generators.
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2022-11-30
Biharmonic hypersurfaces with recurrent operators in the Euclidean space
Esmaiel Abedi, Najma MosadeghAbstract : We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.
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2022-05-31
Constructions of regular sparse anti-magic squares
Guangzhou Chen
, Wen Li, Bangying Xin, Ming ZhongAbstract : For positive integers $n$ and $d$ with $d
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2023-01-31
The nilpotency of the prime radical of a Goldie module
John A. Beachy, Mauricio Medina-B\'arcenasAbstract : With the notion of prime submodule defined by F. Raggi et al. we prove that the intersection of all prime submodules of a Goldie module $M$ is a nilpotent submodule provided that $M$ is retractable and $M^{(\Lambda)}$-projective for every index set $\Lambda$. This extends the well known fact that in a left Goldie ring the prime radical is nilpotent.
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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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2023-01-31
UN rings and group rings
Kanchan Jangra, Dinesh UdarAbstract : A ring $R$ is called a UN ring if every non unit of it can be written as product of a unit and a nilpotent element. We obtain results about lifting of conjugate idempotents and unit regular elements modulo an ideal $I$ of a UN ring $R$. Matrix rings over UN rings are discussed and it is obtained that for a commutative ring $R$, a matrix ring $M_n(R)$ is UN if and only if $R$ is UN. Lastly, UN group rings are investigated and we obtain the conditions on a group $G$ and a field $K$ for the group algebra $KG$ to be UN. Then we extend the results obtained for $KG$ to the group ring $RG$ over a ring $R$ (which may not necessarily be a field).
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2022-11-30
On the Pocklington-Peralta square root algorithm in finite fields
Chang Heon Kim, Namhun Koo, Soonhak KwonAbstract : We present a new square root algorithm in finite fields which is a variant of the Pocklington-Peralta algorithm. We give the complexity of the proposed algorithm in terms of the number of operations (multiplications) in finite fields, and compare the result with other square root algorithms, the Tonelli-Shanks algorithm, the Cipolla-Lehmer algorithm, and the original Pocklington-Peralta square root algorithm. Both the theoretical estimation and the implementation result imply that our proposed algorithm performs favorably over other existing algorithms. In particular, for the NIST suggested field P-224, we show that our proposed algorithm is significantly faster than other proposed algorithms.
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2023-07-31
Dynamics of random dynamical systems
Enkhbayar Azjargal, Zorigt Choinkhor, Nyamdavaa TsegmidAbstract : In this paper, we introduce the concept of $\omega$-expansive of random map on compact metric spaces $\mathcal{P}$. Also we introduce the definitions of positively, negatively shadowing property and shadowing property for two-sided RDS. Then we show that if $\varphi$ is $\omega$-expansive and has the shadowing property for $\omega$, then $\varphi$ is topologically stable for $\omega$.
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2022-11-30
Dually flat and projectively flat Finsler warped product structures
Xiaoling Zhang, Xuesong Zhang, Lili ZhaoAbstract : In this paper, we study the Finsler warped product metric which is dually flat or projectively flat. The local structures of these metrics are completely determined. Some examples are presented.
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Pricing American lookback options under a stochastic volatility model
Donghyun Kim, Junhui Woo, Ji-Hun Yoon
Bull. Korean Math. Soc. 2023; 60(2): 361-388
https://doi.org/10.4134/BKMS.b220134 -
Computation of Wedderburn decomposition of groups algebras from their subalgebra
Gaurav Mittal, Rajendra Kumar Sharma
Bull. Korean Math. Soc. 2022; 59(3): 781-787
https://doi.org/10.4134/BKMS.b210478 -
Some remarks on problems of subset sum
Min Tang, Hongwei Xu
Bull. Korean Math. Soc. 2022; 59(6): 1339-1348
https://doi.org/10.4134/BKMS.b210262 -
Some new classes of zero-difference balanced functions and related constant composition codes
Sankhadip Roy
Bull. Korean Math. Soc. 2022; 59(6): 1327-1337
https://doi.org/10.4134/BKMS.b210183
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On semi-regular injective modules and strong dedekind rings
Renchun Qu
Bull. Korean Math. Soc. 2023; 60(4): 1071-1083
https://doi.org/10.4134/BKMS.b220516 -
On the $p$-adic valuation of generalized harmonic numbers
Çağatay Altuntaş
Bull. Korean Math. Soc. 2023; 60(4): 933-955
https://doi.org/10.4134/BKMS.b220399 -
Automorphisms of K3 surfaces with Picard number two
Kwangwoo Lee
Bull. Korean Math. Soc. 2023; 60(6): 1427-1437
https://doi.org/10.4134/BKMS.b220371 -
$A_{\alpha}$-spectral extrema of graphs with given size and matching number
Xingyu Lei, Shuchao Li, Jianfeng Wang
Bull. Korean Math. Soc. 2023; 60(4): 873-893
https://doi.org/10.4134/BKMS.b220340
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