Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
Most Read
HOME
VIEW ARTICLES
Most Read
VIEW ARTICLES
Most Read
-
2023-03-01
On $S$-multiplication rings
Mohamed Chhiti, Soibri MoindzeAbstract : Let $R$ be a commutative ring with identity and $S$ be a multiplicatively closed subset of $R$. In this article we introduce a new class of ring, called $S$-multiplication rings which are $S$-versions of multiplication rings. An $R$-module $M$ is said to be $S$-multiplication if for each submodule $N$ of $M$, $sN\subseteq JM\subseteq N$ for some $s\in S$ and ideal $J$ of $R$ (see for instance [4, Definition 1]). An ideal $I$ of $R$ is called $S$-multiplication if $I$ is an $S$-multiplication $R$-module. A commutative ring $R$ is called an $S$-multiplication ring if each ideal of $R$ is $S$-multiplication. We characterize some special rings such as multiplication rings, almost multiplication rings, arithmetical ring, and $S$-$PIR$. Moreover, we generalize some properties of multiplication rings to $S$-multiplication rings and we study the transfer of this notion to various context of commutative ring extensions such as trivial ring extensions and amalgamated algebras along an ideal.
-
2024-01-01
Periodic surface homeomorphisms and contact structures
Dheeraj Kulkarni, Kashyap Rajeevsarathy, Kuldeep SahaAbstract : In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.
-
2023-03-01
Relative Rota-Baxter systems on Leibniz algebras
Apurba Das, Shuangjian GuoAbstract : In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This allows us to define a cohomology theory associated with a relative Rota-Baxter system. Finally, we study formal deformations and extendibility of finite order deformations of a relative Rota-Baxter system in terms of the cohomology theory.
-
2023-03-01
Unconditional stability and convergence of fully discrete FEM for the viscoelastic Oldroyd flow with an introduced auxiliary variable
Huifang Zhang, Tong ZhangAbstract : In this paper, a fully discrete numerical scheme for the viscoelastic Oldroyd flow is considered with an introduced auxiliary variable. Our scheme is based on the finite element approximation for the spatial discretization and the backward Euler scheme for the time discretization. The integral term is discretized by the right trapezoidal rule. Firstly, we present the corresponding equivalent form of the considered model, and show the relationship between the origin problem and its equivalent system in finite element discretization. Secondly, unconditional stability and optimal error estimates of fully discrete numerical solutions in various norms are established. Finally, some numerical results are provided to confirm the established theoretical analysis and show the performances of the considered numerical scheme.
-
2023-07-01
Some algebras having relations like those for the 4-dimensional Sklyanin algebras
Alexandru Chirvasitu, S. Paul SmithAbstract : The 4-dimensional Sklyanin algebras are a well-studied 2-parameter family of non-commutative graded algebras, often denoted $A(E,\tau)$, that depend on a quartic elliptic curve $E \subseteq \mathbb{P}^3$ and a translation automorphism $\tau$ of $E$. They are graded algebras generated by four degree-one elements subject to six quadratic relations and in many important ways they behave like the polynomial ring on four indeterminates except that they are not commutative. They can be seen as ``elliptic analogues'' of the enveloping algebra of $\mathfrak{gl}(2,\mathbb{C})$ and the quantized enveloping algebras $U_q(\mathfrak{gl}_2)$. Recently, Cho, Hong, and Lau conjectured that a certain 2-parameter family of algebras arising in their work on homological mirror symmetry consists of 4-dimensional Sklyanin algebras. This paper shows their conjecture is false in the generality they make it. On the positive side, we show their algebras exhibit features that are similar to, and differ from, analogous features of the 4-dimensional Sklyanin algebras in interesting ways. We show that most of the Cho-Hong-Lau algebras determine, and are determined by, the graph of a bijection between two 20-point subsets of the projective space $\mathbb{P}^3$. The paper also examines a 3-parameter family of 4-generator 6-relator algebras admitting presentations analogous to those of the 4-dimensional Sklyanin algebras. This class includes the 4-dimensional Sklyanin algebras and most of the Cho-Hong-Lau algebras.
-
2023-01-01
Two-weighted conditions and characterizations for a class of multilinear fractional new maximal operators
Rui Li, Shuangping TaoAbstract : In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator $\mathcal{M}_{\varphi,\beta}$ are established. Meanwhile, we introduce the $S_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ conditions and obtain the characterization of two-weighted inequalities for $\mathcal{M}_{\varphi,\beta}$. Finally, the relationships of the conditions $S_{(\vec{p},q),\beta}(\varphi)$, $\mathcal{A}_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ and the characterization of the one-weight $A_{(\vec{p},q),\beta}(\varphi)$ are given.
-
2023-07-01
Cup product on relative bounded cohomology
HeeSook ParkAbstract : In this paper, we define cup product on relative bounded cohomology, and study its basic properties. Then, by extending it to a more generalized formula, we prove that all cup products of bounded cohomology classes of an amalgamated free product \( G_{1}\ast_{A}G_{2} \) are zero for every positive degree, assuming that free factors \( G_i \) are amenable and amalgamated subgroup \( A \) is normal in both of them. As its consequences, we show that all cup products of bounded cohomology classes of the groups \( \mathbb{Z} \ast \mathbb{Z} \) and \( \mathbb{Z}_{n} \ast_{\mathbb{Z}_{d}}\mathbb{Z}_m \), where \( d \) is the greatest common divisor of \( n \) and \( m \), are zero for every positive degree.
-
2023-03-01
The Harbourne-Hirschowitz condition and the anticanonical orthogonal property for surfaces
Abel Castorena, Juan Bosco Fr\'ias-MedinaAbstract : In this paper we give the first steps toward the study of the Harbourne-Hirschowitz condition and the anticanonical orthogonal property for regular surfaces. To do so, we consider the Kodaira dimension of the surfaces and study the cases based on the Enriques-Kodaira classification.
-
2023-07-01
Preresolving subcategories in extriangulated categories
Songsong Liu, Jiaqun WeiAbstract : In this paper, we introduce and study preresolving subcategories in an extriangulated category~$\mathscr{C}$. Let $\mathcal{Y}$ be a $\mathcal{Z}$-preresolving subcategory of $\mathscr{C}$ admitting a $\mathcal{Z}$-proper $\xi$-generator $\mathcal{X}$. We give the characterization of $\mathcal{Z}\text{-}{\rm proper}~\mathcal{Y}$-resolution dimension of an object in $\mathscr{C}$. Next, for an object $A$ in $\mathscr{C}$, if the $\mathcal{Z}\text{-}{\rm proper}~\mathcal{Y}$-resolution~dimension of $A$ is at most $n$, then all ``$n$-$\mathcal{X}$-syzygies" of $A$ are objects in $\mathcal{Y}$. Finally, we prove that $A$ has a $\mathcal{Z}$-proper $\mathcal{X}$-resolution if and only if $A$ has a $\mathcal{Z}$-proper $\mathcal{Y}$-resolution. As an application, we introduce $(\mathcal{X},\mathcal{Z})$-Gorenstein~subcategory $\mathcal{GX}_{\mathcal{Z}}(\xi)$ of $\mathscr{C}$ and prove that $\mathcal{GX}_{\mathcal{Z}}(\xi)$ is both $\mathcal{Z}$-resolving subcategory and $\mathcal{Z}$-coresolving subcategory of $\mathscr{C}$.
-
2024-01-01
Gorenstein $FP_{n}$-injective modules with respect to a semidualizing bimodule
Zhiqiang Cheng, Guoqiang ZhaoAbstract : Let $S$ and $R$ be rings and $_{S}C_{R}$ a semidualizing bimodule. We introduce the notion of $G_C$-$FP_n$-injective modules, which generalizes $G_C$-$FP$-injective modules and $G_C$-weak injective modules. The homological properties and the stability of $G_C$-$FP_n$-injective modules are investigated. When $S$ is a left $n$-coherent ring, several nice properties and new Foxby equivalences relative to $G_C$-$FP_n$-injective modules are given.
Most Read
-
On uniformly $S$-absolutely pure modules
Xiaolei Zhang
J. Korean Math. Soc. 2023; 60(3): 521-536
https://doi.org/10.4134/JKMS.j220055 -
Minimal surface system in Euclidean four-space
Hojoo Lee
J. Korean Math. Soc. 2023; 60(1): 71-90
https://doi.org/10.4134/JKMS.j220095 -
Two new recurrent levels and chaotic dynamics of $\mathbb{Z}^d_+$-actions
Shaoting Xie, Jiandong Yin
J. Korean Math. Soc. 2022; 59(6): 1229-1254
https://doi.org/10.4134/JKMS.j220202 -
Asymptotic behavior of solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays
Cung The Anh, Vu Manh Toi, Phan Thi Tuyet
J. Korean Math. Soc. 2024; 61(2): 227-253
https://doi.org/10.4134/JKMS.j220380
Most Downloaded
-
Continuum-wise expansiveness for $C^1$ generic vector fields
Manseob Lee
J. Korean Math. Soc. 2023; 60(5): 987-998
https://doi.org/10.4134/JKMS.j220359 -
The Bongartz's theorem of Gorenstein cosilting complexes
Hailou Yao, Qianqian Yuan
J. Korean Math. Soc. 2023; 60(6): 1337-1364
https://doi.org/10.4134/JKMS.j230208 -
Low rank orthogonal bundles and quadric fibrations
Insong Choe, George H. Hitching
J. Korean Math. Soc. 2023; 60(6): 1137-1169
https://doi.org/10.4134/JKMS.j220125 -
The first positive and negative Dirac eigenvalues on Sasakian manifolds
Eui Chul Kim
J. Korean Math. Soc. 2023; 60(5): 999-1021
https://doi.org/10.4134/JKMS.j220480
Editorial Office
✕
JKMS
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd