Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2024-05-31
A Gorenstein homological characterization of Krull domains
Shiqi Xing, Xiaolei ZhangAbstract : In this note, we shed new light on Krull domains from the point view of Gorenstein homological algebra. By using the so-called $w$-operation, we show that an integral domain $R$ is Krull if and only if for any nonzero proper $w$-ideal $I$, the Gorenstein global dimension of the $w$-factor ring $(R/I)_{w}$ is zero. Further, we obtain that an integral domain $R$ is Dedekind if and only if for any nonzero proper ideal $I$, the Gorenstein global dimension of the factor ring $R/I$ is zero.
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2023-09-30
Sharp inequalities involving the Chen-Ricci inequality for slant Riemannian submersions
Mehmet Akif Akyol, Nergiz (Önen) PoyrazAbstract : Main objective of the present paper is to establish Chen inequalities for slant Riemannian submersions in contact geometry. In this manner, we give some examples for slant Riemannian submersions and also investigate some curvature relations between the total space, the base space and fibers. Moreover, we establish Chen-Ricci inequalities on the vertical and the horizontal distributions for slant Riemannian submersions from Sasakian space forms.
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2024-07-31
Schatten classes of composition operators on Dirichlet Type Spaces with Superharmonic weights
Zuoling LiuAbstract : In this paper, we completely characterize the Schatten classes of composition operators on the Dirichlet type spaces with superharmonic weights. Our investigation is basced on building a bridge between the Schatten classes of composition operators on the weighted Dirichlet type spaces and Toeplitz operators on weighted Bergman spaces.
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2023-05-31
When all permutations are combinatorial similarities
Viktoriia Bilet, Oleksiy DovgosheyAbstract : Let \((X, d)\) be a semimetric space. A permutation \(\Phi\) of the set \(X\) is a combinatorial self similarity of \((X, d)\) if there is a bijective function \(f \colon d(X \times X) \to d(X \times X)\) such that \[ d(x, y) = f(d(\Phi(x), \Phi(y))) \] for all \(x\), \(y \in X\). We describe the set of all semimetrics \(\rho\) on an arbitrary nonempty set \(Y\) for which every permutation of \(Y\) is a combinatorial self similarity of \((Y, \rho)\).
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2024-05-31
Residual $p$-finiteness of certain HNN extensions of free abelian groups of finite rank
Chiew Khiam Tang, Peng Choon WongAbstract : Let $p$ be a prime. A group $G$ is said to be residually $p$-finite if for each non-trivial element $x$ of $G$, there exists a normal subgroup $N$ of index a power of $p$ in $G$ such that $x$ is not in $N$. In this note we shall prove that certain HNN extensions of free abelian groups of finite rank are residually $p$-finite. In addition some of these HNN extensions are subgroup separable. Characterisations for certain one-relator groups and similar groups including the Baumslag-Solitar groups to be residually $p$-finite are proved.
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2023-05-31
The classification of $\omega$-left-symmetric algebras in low dimensions
Zhiqi Chen, Yang WuAbstract : $\omega$-left-symmetric algebras contain left-symmetric algebras as a subclass and the commutator defines an $\omega$-Lie algebra. In this paper, we classify $\omega$-left-symmetric algebras in dimension 3 up to an isomorphism based on the classification of $\omega$-Lie algebras and the technique of Lie algebras.
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2024-05-31
On the growth of algebroid solutions of algebraic differential equations
Manli Liu, Linlin WuAbstract : Using the Nevanlinna value distribution theory of algebroid functions, this paper investigates the growth of two types of complex algebraic differential equation with algebroid solutions and obtains two results, which extend the growth of complex algebraic differential equation with meromorphic solutions obtained by Gao [4].
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2023-07-31
Toeplitz-type operators on the Fock space $F_{\alpha}^{2}$
Chunxu Xu, Tao YuAbstract : Let $j$ be a nonnegative integer. We define the Toeplitz-type operators $T_{a}^{(j)}$ with symbol $a\in L^{\infty}(C)$, which are variants of the traditional Toeplitz operators obtained for $j=0$. In this paper, we study the boundedness of these operators and characterize their compactness in terms of its Berezin transform.
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2023-09-30
Weak potency and cyclic subgroup separability of certain free products and tree products
Muhammad Sufi Mohd Asri, Wan Ainun Mior Othman, Kok Bin Wong, Peng Choon WongAbstract : In this note, we shall show that the generalized free products of subgroup separable groups amalgamating a subgroup which itself is a finite extension of a finitely generated normal subgroup of both the factor groups are weakly potent and cyclic subgroup separable. Then we apply our result to generalized free products of finite extensions of finitely generated torsion-free nilpotent groups. Finally, we shall show that their tree products are cyclic subgroup separable.
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2024-05-31
A non-Newtonian approach in differential geometry of curves: multiplicative rectifying curves
Muhittin Evren Aydın
, Aykut Has , Beyhan Yılmaz Abstract : In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension $3$, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.
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Homology and Serre class in $\mathrm{D}(R)$
Zhicheng Wang
Bull. Korean Math. Soc. 2023; 60(1): 23-32
https://doi.org/10.4134/BKMS.b210703 -
Partial sums and inclusion relations for starlike functions associated with an evolute of a nephroid curve
Gurpreet Kaur, Sumit Nagpal
Bull. Korean Math. Soc. 2023; 60(6): 1477-1496
https://doi.org/10.4134/BKMS.b220582 -
S-curvature and geodesic orbit property of invariant $(\alpha_{1},\alpha_{2})$-metrics on spheres
Huihui An, Zaili Yan, Shaoxiang Zhang
Bull. Korean Math. Soc. 2023; 60(1): 33-46
https://doi.org/10.4134/BKMS.b210835 -
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
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Prime-producing polynomials related to class number one problem of number fields
Jun Ho Lee
Bull. Korean Math. Soc. 2023; 60(2): 315-323
https://doi.org/10.4134/BKMS.b220094 -
$p$-Biharmonic hypersurfaces in Einstein space and conformally flat space
Ahmed Mohammed Cherif, Khadidja Mouffoki
Bull. Korean Math. Soc. 2023; 60(3): 705-715
https://doi.org/10.4134/BKMS.b220347 -
Partial sums and inclusion relations for starlike functions associated with an evolute of a nephroid curve
Gurpreet Kaur, Sumit Nagpal
Bull. Korean Math. Soc. 2023; 60(6): 1477-1496
https://doi.org/10.4134/BKMS.b220582 -
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
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