Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-09-30
Structure of idempotents in polynomial rings and matrix rings
Juan Huang, Tai Keun Kwak, Yang Lee, Zhelin PiaoAbstract : An idempotent $e$ of a ring $R$ is called {\it right} (resp., {\it left}) {\it semicentral} if $er=ere$ (resp., $re =ere$) for any $r\in R$, and an idempotent $e$ of $R\backslash \{0,1\}$ will be called {\it right} (resp., {\it left}) {\it quasicentral} provided that for any $r\in R$, there exists an idempotent $f=f(e,r)\in R\backslash \{0,1\}$ such that $er=erf$ (resp., $re=fre$). We show the whole shapes of idempotents and right (left) semicentral idempotents of upper triangular matrix rings and polynomial rings. We next prove that every nontrivial idempotent of the $n$ by $n$ full matrix ring over a principal ideal domain is right and left quasicentral and, applying this result, we can find many right (left) quasicentral idempotents but not right (left) semicentral.
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2024-03-31
Wavelet characterizations of variable Hardy-Lorentz spaces
Yao HeAbstract : In this paper, let $q\in(0,1]$. We establish the boundedness of intrinsic $g$-functions from the Hardy-Lorentz spaces with variable exponent ${H}^{p(\cdot),q}(\mathbb R^{n})$ into Lorentz spaces with variable exponent ${L}^{p(\cdot),q}(\mathbb R^{n})$. Then, for any $q\in(0,1]$, via some estimates on a discrete Littlewood-Paley $g$-function and a Peetre-type maximal function, we obtain several equivalent characterizations of ${H}^{p(\cdot),q}(\mathbb R^{n})$ in terms of wavelets.
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2024-03-31
On the generalized principally injective modules
Fatemeh Gholami, Zohreh Habibi, Alireza NajafizadehAbstract : Some results are generalized from principally injective rings to principally injective modules. Moreover, it is proved that the results are valid to some other extended injectivity conditions which may be defined over modules. The influence of such injectivity conditions are studied for both the trace and the reject submodules of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.
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2023-05-31
An altered group ring construction of the $[24,12,8]$ and $[48,24,12]$ Type II linear block code
Shefali Gupta, Dinesh UdarAbstract : In this paper, we present a new construction for self-dual codes that uses the concept of double bordered construction, group rings, and reverse circulant matrices. Using groups of orders $2,3,4,$ and $5$, and by applying the construction over the binary field and the ring $F_{2}+uF_{2}$, we obtain extremal binary self-dual codes of various lengths: $12, 16, 20, 24, 32, 40,$ and $48$. In particular, we show the significance of this new construction by constructing the unique Extended Binary Golay Code $[24,12,8]$ and the unique Extended Quadratic Residue $[48,24,12]$ Type II linear block code. Moreover, we strengthen the existing relationship between units and non-units with the self-dual codes presented in [10] by limiting the conditions given in the corollary. Additionally, we establish a relationship between idempotent and self-dual codes, which is done for the first time in the literature.
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2023-05-31
On a Spitzer-type law of large numbers for partial sums of independent and identically distributed random variables under sub-linear expectations
Miaomiao Wang, Min Wang, Xuejun WangAbstract : In this paper, under some suitable conditions, we study the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables in upper expectation space. Some general results on necessary and sufficient conditions of the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables under sub-linear expectations are established, which extend the corresponding ones in classic probability space to the case of sub-linear expectation space.
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2023-01-31
Stability of bifurcating stationary periodic solutions of the generalized Swift--Hohenberg equation
Soyeun JungAbstract : Applying the Lyapunov--Schmidt reduction, we consider \linebreak spectral stability of small amplitude stationary periodic solutions bifurcating from an equilibrium of the generalized Swift--Hohenberg equation. We follow the mathematical framework developed in [15, 16, 19, 23] to construct such periodic solutions and to determine regions in the parameter space for which they are stable by investigating the movement of the spectrum near zero as parameters vary.
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2023-05-31
$p$-Biharmonic hypersurfaces in Einstein space and conformally flat space
Ahmed Mohammed Cherif, Khadidja MouffokiAbstract : In this paper, we present some new properties for $p$-biharmon\-ic hypersurfaces in a Riemannian manifold. We also characterize the $p$-biharmonic submanifolds in an Einstein space. We construct a new example of proper $p$-biharmonic hypersurfaces. We present some open problems.
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2024-01-31
Stability of total scalar curvature and the critical point equation
Seungsu Hwang, Gabjin YunAbstract : We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.
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2024-05-31
2-local derivations on C$^{\ast}$-algebras
Wenbo Huang
, Jiankui LiAbstract : In this paper, we prove that every 2-local derivation on several classes of C$^{\ast}$-algebras, such as unital properly infinite, type $\mathrm{I}$ or residually finite-dimensional C$^{\ast}$-algebras, is a derivation. We show that the following statements are equivalent: (1) every 2-local derivation on a C$^{\ast}$-algebra is a derivation, (2) every 2-local derivation on a unital primitive antiliminal and no properly infinite C$^{\ast}$-algebra is a derivation. We also show that every 2-local derivation on a group C$^{\ast}$-algebra $C^{\ast}(\mathbb{F})$ or a unital simple infinite-dimensional quasidiagonal C$^{\ast}$-algebra, which is stable finite antiliminal C$^{\ast}$-algebra, is a derivation.
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2023-01-31
New families of hyperbolic twisted torus knots with generalized torsion
Keisuke Himeno, Masakazu TeragaitoAbstract : A generalized torsion element is an obstruction for a group to admit a bi-ordering. Only a few classes of hyperbolic knots are known to admit such an element in their knot groups. Among twisted torus knots, the known ones have their extra twists on two adjacent strands of torus knots. In this paper, we give several new families of hyperbolic twisted torus knots whose knot groups have generalized torsion. They have extra twists on arbitrarily large numbers of adjacent strands of torus knots.
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Some estimates for generalized commutators of multilinear Calder\'on-Zygmund operators
Honghai Liu, Zengyan Si, Ling Wang
Bull. Korean Math. Soc. 2023; 60(2): 541-560
https://doi.org/10.4134/BKMS.b220287 -
Commutators of the maximal functions on Banach function spaces
Müjdat Ağcayazı, Pu Zhang
Bull. Korean Math. Soc. 2023; 60(5): 1391-1408
https://doi.org/10.4134/BKMS.b220724 -
$S$-versions and $S$-generalizations of idempotents, pure ideals and Stone type theorems
Bayram Ali Ersoy, Ünsal Tekir, Eda Yıldız
Bull. Korean Math. Soc. 2024; 61(1): 83-92
https://doi.org/10.4134/BKMS.b230023 -
Some results on meromorphic solutions of q-difference differential equations
Lingyun Gao, Zhenguang Gao, Manli Liu
Bull. Korean Math. Soc. 2023; 60(3): 593-610
https://doi.org/10.4134/BKMS.b210773
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Copure projective modules over FGV-domains and Gorenstein Pr\"{u}fer domains
Shiqi Xing
Bull. Korean Math. Soc. 2023; 60(4): 971-983
https://doi.org/10.4134/BKMS.b220431 -
When all permutations are combinatorial similarities
Viktoriia Bilet, Oleksiy Dovgoshey
Bull. Korean Math. Soc. 2023; 60(3): 733-746
https://doi.org/10.4134/BKMS.b220355 -
The $u$-$S$-global dimensions of commutative rings
Wei Qi, Xiaolei Zhang
Bull. Korean Math. Soc. 2023; 60(6): 1523-1537
https://doi.org/10.4134/BKMS.b220677 -
Representations over Green algebras of weak Hopf algebras based on Taft algebras
Liufeng Cao
Bull. Korean Math. Soc. 2023; 60(6): 1687-1695
https://doi.org/10.4134/BKMS.b220845
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