Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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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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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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2023-01-31
Homology and Serre class in $\mathrm{D}(R)$
Zhicheng WangAbstract : Let $\mathcal{S}$ be a Serre class in the category of modules and $\mathfrak{a}$ an ideal of a commutative Noetherian ring $R$. We study the containment of Tor modules, Koszul homology and local homology in $\mathcal{S}$ from below. With these results at our disposal, by specializing the Serre class to be Noetherian or zero, a handful of conclusions on Noetherianness and vanishing of the foregoing homology theories are obtained. We also determine when $\mathrm{Tor}_{s+t}^R(R/\mathfrak{a},X)\cong\mathrm{Tor}_{s}^R(R/\mathfrak{a},\mathrm{H}_{t}^\mathfrak{a}(X))$.
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2022-05-31
The characterisation of $BMO$ via commutators in variable Lebesgue spaces on stratified groups
Dongli Liu, Jian Tan, Jiman ZhaoAbstract : Let $T$ be a bilinear Calder\'{o}n-Zygmund operator, $$b\in \cup_{q>1}L_{loc}^{q}(G).$$ We firstly obtain a constructive proof of the weak factorisation of Hardy spaces. Then we establish the characterization of $BMO$ spaces by the boundedness of the commutator $[b, T]_{j}$ in variable Lebesgue spaces.
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2023-03-31
A note on comparison principle for elliptic obstacle problems with $L^{1}$-data
Kyeong Song, Yeonghun YounAbstract : In this note, we study a comparison principle for elliptic obstacle problems of $p$-Laplacian type with $L^1$-data. As a consequence, we improve some known regularity results for obstacle problems with zero Dirichlet boundary conditions.
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2024-01-31
$S$-versions and $S$-generalizations of idempotents, pure ideals and Stone type theorems
Bayram Ali Ersoy, Ünsal Tekir, Eda YıldızAbstract : Let $R$ be a commutative ring with nonzero identity and $M$ be an $R$-module. In this paper, we first introduce the concept of $S$-idempotent element of $R$. Then we give a relation between $S$-idempotents of $R$ and clopen sets of $S$-Zariski topology. After that we define $S$-pure ideal which is a generalization of the notion of pure ideal. In fact, every pure ideal is $S$-pure but the converse may not be true. Afterwards, we show that there is a relation between $S$-pure ideals of $R$ and closed sets of $S$-Zariski topology that are stable under generalization.
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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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2024-01-31
Periodic shadowable points
Namjip Koo, Hyunhee Lee, Nyamdavaa TsegmidAbstract : In this paper, we consider the set of periodic shadowable points for homeomorphisms of a compact metric space, and we prove that this set satisfies some properties such as invariance and being a $G_{\delta}$ set. Then we investigate implication relations related to sets consisting of shadowable points, periodic shadowable points and uniformly expansive points, respectively. Assume that the set of periodic points and the set of periodic shadowable points of a homeomorphism on a compact metric space are dense in $X$. Then we show that a homeomorphism has the periodic shadowing property if and only if so is the restricted map to the set of periodic shadowable points. We also give some examples related to our results.
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2022-07-31
Integrability of an almost complex structure on $S^4\times_f V^2$
Jong Taek Cho, Sun Hyang Chun, Yunhee EuhAbstract : In this paper, we prove that any orthogonal almost complex structure on a warped product manifold of any oriented closed surface and a round 4-sphere for a concircular warping function on the sphere is never integrable. This gives a partial answer to Calabi's problem.
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2024-01-31
A note on variation continuity for multilinear maximal operators
Xiao ZhangAbstract : This note is devoted to establishing the variation continuity of the one-dimensional discrete uncentered multilinear maximal operator. The above result is based on some refine variation estimates of the above maximal functions on monotone intervals. The main result essentially improves some known ones.
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Irreducibility of the moduli space for the quotient singularity $\frac{1}{2k+1}(k+1,1,2k)$
Seung-Jo Jung
Bull. Korean Math. Soc. 2022; 59(6): 1409-1422
https://doi.org/10.4134/BKMS.b210797 -
On toric Hamiltonian $T$-spaces with anti-symplectic involutions
Jin Hong Kim
Bull. Korean Math. Soc. 2022; 59(3): 671-683
https://doi.org/10.4134/BKMS.b210406 -
A note on Artinian local rings
Kui Hu, Hwankoo Kim, Dechuan Zhou
Bull. Korean Math. Soc. 2022; 59(5): 1317-1325
https://doi.org/10.4134/BKMS.b210759 -
Multiplicative functions commutable with binary quadratic forms $x^2 \pm xy + y^2$
Poo-Sung Park
Bull. Korean Math. Soc. 2023; 60(1): 75-81
https://doi.org/10.4134/BKMS.b210915
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Uniqueness results on meromorphic functions and their difference operators sharing targets with weight
Thu Thuy Hoang, Hong Nhat Nguyen, Duc Thoan Pham
Bull. Korean Math. Soc. 2023; 60(2): 461-473
https://doi.org/10.4134/BKMS.b220190 -
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 -
Estimate for bilinear Calder\'{o}n-Zygmund operator and its commutator on product of variable exponent spaces
Guanghui Lu, Shuangping Tao
Bull. Korean Math. Soc. 2022; 59(6): 1471-1493
https://doi.org/10.4134/BKMS.b210839
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