Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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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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2022-09-30
On almost quasi-coherent rings and almost von Neumann rings
Haitham El Alaoui, Mourad El Maalmi, Hakima MouanisAbstract : Let $R$ be a commutative ring with identity. We call the ring $R$ to be an almost quasi-coherent ring if for any finite set of elements $a_{1},\dots,a_{p}$ and $a$ of $R$, there exists a positive integer $m$ such that the ideals $\bigcap_{i=1}^p Ra_{i}^{m}$ and $Ann_{R}(a^{m})$ are finitely generated, and to be almost von Neumann regular rings if for any two elements $a$ and $b$ in $R$, there exists a positive integer $n$ such that the ideal $(a^{n}, b^{n})$ is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.
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2023-03-31
The catenary degree of the saturated numerical semigroups with prime multiplicity
Meral S\"{u}er
Abstract : In this paper, we formulate the set of all saturated numerical semigroups with prime multiplicity. We characterize the catenary degrees of elements of the semigroups we obtained which are important invariants in factorization theory. We also give the proper characterizations of the semigroups under consideration.
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2022-09-30
A note on $\phi$-Pr\"{u}fer $v$-multiplication rings
Xiaolei ZhangAbstract : In this note, we show that a strongly $\phi$-ring $R$ is a $\phi$-$\rm PvMR$ if and only if any $\phi$-torsion-free $R$-module is $\phi$-$w$-flat, if and only if any $\rm GV$-torsion-free divisible $R$-module is nonnil-absolutely $w$-pure, if and only if any $\rm GV$-torsion-free $h$-divisible $R$-module is nonnil-absolutely $w$-pure, if and only if any finitely generated nonnil ideal of $R$ is $w$-projective.
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2023-03-31
On nuclearity of semigroup crossed products
Qing MengAbstract : In this paper, we study nuclearity of semigroup crossed products for quasi-lattice ordered groups. We show the relationships among nuclearity of the semigroup crossed product, amenability of the quasi-lattice ordered group and nuclearity of the underlying $C^*$-algebra.
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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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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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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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2023-07-31
On semi-regular injective modules and strong dedekind rings
Renchun QuAbstract : The main motivation of this paper is to introduce and study the notions of strong Dedekind rings and semi-regular injective modules. Specifically, a ring $R$ is called strong Dedekind if every semi-regular ideal is $Q_0$-invertible, and an $R$-module $E$ is called a semi-regular injective module provided ${\rm Ext}^1_R(T,E)=0$ for every $\mathcal{Q}$-torsion module $T$. In this paper, we first characterize rings over which all semi-regular injective modules are injective, and then study the semi-regular injective envelopes of $R$-modules. Moreover, we introduce and study the semi-regular global dimensions $sr$-gl.dim$(R)$ of commutative rings $R$. Finally, we obtain that a ring $R$ is a ${\rm DQ}$-ring if and only if $sr$-gl.dim$(R)=0$, and a ring $R$ is a strong Dedekind ring if and only if $sr$-gl.dim$(R)\leq 1$, if and only if any semi-regular ideal is projective. Besides, we show that the semi-regular dimensions of strong Dedekind rings are at most one.
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2022-09-30
Basic formulas for the double integral transform of functionals on abstract Wiener space
Hyun Soo ChungAbstract : In this paper, we establish several basic formulas among the double-integral transforms, the double-convolution products, and the inverse double-integral transforms of cylinder functionals on abstract Wiener space. We then discuss possible relationships involving the double-integral transform.
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Dynamics of random dynamical systems
Enkhbayar Azjargal, Zorigt Choinkhor, Nyamdavaa Tsegmid
Bull. Korean Math. Soc. 2023; 60(4): 1131-1139
https://doi.org/10.4134/BKMS.b220595 -
Continuous data assimilation for the three-dimensional Leray-$\alpha$ model with stochastically noisy data
Bui Kim My
, Tran Quoc TuanBull. Korean Math. Soc. 2023; 60(1): 93-111
https://doi.org/10.4134/BKMS.b210919 -
A note on the properties of pseudo-weighted Browder spectrum
Preeti Dharmarha, Sarita Kumari
Bull. Korean Math. Soc. 2023; 60(1): 123-135
https://doi.org/10.4134/BKMS.b210931 -
Complex symmetric weighted composition-differentiation operators on $H^2$
Lian Hu, Songxiao Li, Rong Yang
Bull. Korean Math. Soc. 2023; 60(5): 1141-1154
https://doi.org/10.4134/BKMS.b220215
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Single step real-valued iterative method for linear system of equations with complex symmetric matrices
Jingjing Cui, Zhengge Huang, Beibei Li, Xiaofeng Xie
Bull. Korean Math. Soc. 2023; 60(5): 1181-1199
https://doi.org/10.4134/BKMS.b220524 -
Weighted integral inequalities for modified integral Hardy operators
Duranta Chutia, Rajib Haloi
Bull. Korean Math. Soc. 2022; 59(3): 757-780
https://doi.org/10.4134/BKMS.b210469 -
Anti-flips of the blow-ups of the projective spaces at torus invariant points
Hiroshi Sato, Shigehito Tsuzuki
Bull. Korean Math. Soc. 2023; 60(6): 1705-1714
https://doi.org/10.4134/BKMS.b220864 -
Volume density asymptotics of central harmonic spaces
Peter Gilkey, JeongHyeong Park
Bull. Korean Math. Soc. 2023; 60(6): 1539-1553
https://doi.org/10.4134/BKMS.b220735
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