A ring R is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L. Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if R is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.
{"title":"SOME NEW CHARACTERIZATIONS OF QUASI-FROBENIUS RINGS BY USING PURE-INJECTIVITY","authors":"A. MORADZADEH-DEHKORDI","doi":"10.4134/BKMS.B190247","DOIUrl":"https://doi.org/10.4134/BKMS.B190247","url":null,"abstract":"A ring R is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L. Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if R is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"371-381"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.
{"title":"EXACT FORMULA FOR JACOBI-EISENSTEIN SERIES OF SQUARE FREE DISCRIMINANT LATTICE INDEX","authors":"R. Xiong","doi":"10.4134/BKMS.B190342","DOIUrl":"https://doi.org/10.4134/BKMS.B190342","url":null,"abstract":"In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"481-488"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this short paper is to show some rigidity results for the actions of certain finitely presented groups by homeomorphisms. As an interesting and special case, we show that the actions of HigmanThompson groups by homeomorphisms on a cohomology manifold with a non-zero Euler characteristic should be trivial. This is related to the wellknown Zimmer program and shows that the actions by homeomorphism could be very much different from those by diffeomorphisms.
{"title":"ON THE ACTIONS OF HIGMAN-THOMPSON GROUPS BY HOMEOMORPHISMS","authors":"Jin Hong Kim","doi":"10.4134/BKMS.B190316","DOIUrl":"https://doi.org/10.4134/BKMS.B190316","url":null,"abstract":"The aim of this short paper is to show some rigidity results for the actions of certain finitely presented groups by homeomorphisms. As an interesting and special case, we show that the actions of HigmanThompson groups by homeomorphisms on a cohomology manifold with a non-zero Euler characteristic should be trivial. This is related to the wellknown Zimmer program and shows that the actions by homeomorphism could be very much different from those by diffeomorphisms.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"449-457"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we mainly study existence and regularity of mild solutions to the parabolic-elliptic system of drift-diffusion type with small initial data in Fourier-Besov spaces. To be more detailed, we will explain that global-in-time mild solutions are well-posed and Gevrey regular by means of multilinear singular integrals and Fourier localization argument. Furthermore, we can get time decay rate estimate of mild solutions in Fourier-Besov spaces.
{"title":"GEVREY REGULARITY AND TIME DECAY OF THE FRACTIONAL DEBYE-HÜCKEL SYSTEM IN FOURIER-BESOV SPACES","authors":"Yiwen Cui, Weiliang Xiao","doi":"10.4134/BKMS.B191054","DOIUrl":"https://doi.org/10.4134/BKMS.B191054","url":null,"abstract":"In this paper we mainly study existence and regularity of mild solutions to the parabolic-elliptic system of drift-diffusion type with small initial data in Fourier-Besov spaces. To be more detailed, we will explain that global-in-time mild solutions are well-posed and Gevrey regular by means of multilinear singular integrals and Fourier localization argument. Furthermore, we can get time decay rate estimate of mild solutions in Fourier-Besov spaces.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"1393-1408"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70363188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let (R,m) be a Noetherian local Cohen-Macaulay ring and I be a proper ideal of R. Assume that βR(I, R) denotes the constant value of depthR(R/I n) for n 0. In this paper we introduce the new notion γR(I, R) and then we prove the following inequalities: βR(I, R) ≤ γR(I, R) ≤ dimR− cd(I, R) ≤ dimR/I. Also, some applications of these inequalities will be included.
{"title":"A NOTE ON COHOMOLOGICAL DIMENSION OVER COHEN-MACAULAY RINGS","authors":"Iraj Bagheriyeh, K. Bahmanpour, G. Ghasemi","doi":"10.4134/BKMS.B190165","DOIUrl":"https://doi.org/10.4134/BKMS.B190165","url":null,"abstract":"Let (R,m) be a Noetherian local Cohen-Macaulay ring and I be a proper ideal of R. Assume that βR(I, R) denotes the constant value of depthR(R/I n) for n 0. In this paper we introduce the new notion γR(I, R) and then we prove the following inequalities: βR(I, R) ≤ γR(I, R) ≤ dimR− cd(I, R) ≤ dimR/I. Also, some applications of these inequalities will be included.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"275-280"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With the motivation to extend the Zelasko’s theorem on commutative algebras, it was shown in [2] that if n ∈ {3, 4} is fixed, A,B are commutative algebras and h : A → B is an n-Jordan homomorphism, then h is an n-ring homomorphism. In this paper, we extend this result for all n ≥ 3.
{"title":"SOME RESULTS ON n-JORDAN HOMOMORPHISMS","authors":"J. Cheshmavar, S. Hosseini, Choonkill Park","doi":"10.4134/BKMS.B180719","DOIUrl":"https://doi.org/10.4134/BKMS.B180719","url":null,"abstract":"With the motivation to extend the Zelasko’s theorem on commutative algebras, it was shown in [2] that if n ∈ {3, 4} is fixed, A,B are commutative algebras and h : A → B is an n-Jordan homomorphism, then h is an n-ring homomorphism. In this paper, we extend this result for all n ≥ 3.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"136 1","pages":"31-35"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70359659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is concerned with the global behavior of components of radial nodal solutions of semilinear elliptic problems −∆v = λh(x, v) in Ω, v = 0 on ∂Ω, where Ω = {x ∈ RN : r1 < |x| < r2} with 0 < r1 < r2, N ≥ 2. The nonlinear term is continuous and satisfies h(x, 0) = h(x, s1(x)) = h(x, s2(x)) = 0 for suitable positive, concave function s1 and negative, convex function s2, as well as sh(x, s) > 0 for s ∈ R {0, s1(x), s2(x)}. Moreover, we give the intervals for the parameter λ which ensure the existence and multiplicity of radial nodal solutions for the above problem. For this, we use global bifurcation techniques to prove our main results.
{"title":"NODAL SOLUTIONS FOR AN ELLIPTIC EQUATION IN AN ANNULUS WITHOUT THE SIGNUM CONDITION","authors":"Tianlan Chen, Yanqiong Lu, Ruyun Ma","doi":"10.4134/BKMS.B190227","DOIUrl":"https://doi.org/10.4134/BKMS.B190227","url":null,"abstract":"This paper is concerned with the global behavior of components of radial nodal solutions of semilinear elliptic problems −∆v = λh(x, v) in Ω, v = 0 on ∂Ω, where Ω = {x ∈ RN : r1 < |x| < r2} with 0 < r1 < r2, N ≥ 2. The nonlinear term is continuous and satisfies h(x, 0) = h(x, s1(x)) = h(x, s2(x)) = 0 for suitable positive, concave function s1 and negative, convex function s2, as well as sh(x, s) > 0 for s ∈ R {0, s1(x), s2(x)}. Moreover, we give the intervals for the parameter λ which ensure the existence and multiplicity of radial nodal solutions for the above problem. For this, we use global bifurcation techniques to prove our main results.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"331-343"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper gives a sparse domination for the iterated commutators of multilinear pseudo-differential operators with the symbol σ belonging to the Hörmander class, and establishes the quantitative bounds of the Bloom type estimates for such commutators. Moreover, the Cp estimates for the corresponding multilinear pseudo-differential operators are also obtained.
{"title":"A NOTE ON MULTILINEAR PSEUDO-DIFFERENTIAL OPERATORS AND ITERATED COMMUTATORS","authors":"Yongming Wen, Huo-xiong Wu, Qingying Xue","doi":"10.4134/BKMS.B190532","DOIUrl":"https://doi.org/10.4134/BKMS.B190532","url":null,"abstract":"This paper gives a sparse domination for the iterated commutators of multilinear pseudo-differential operators with the symbol σ belonging to the Hörmander class, and establishes the quantitative bounds of the Bloom type estimates for such commutators. Moreover, the Cp estimates for the corresponding multilinear pseudo-differential operators are also obtained.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"851-864"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let A be an m × n matrix over nonnegative integers. The isolation number of A is the maximum number of isolated entries in A. We investigate linear operators that preserve the isolation number of matrices over nonnegative integers. We obtain that T is a linear operator that strongly preserve isolation number k for 1 ≤ k ≤ min{m,n} if and only if T is a (P,Q)-operator, that is, for fixed permutation matrices P and Q, T (A) = PAQ or, m = n and T (A) = PAtQ for any m× n matrix A, where At is the transpose of A.
设A是一个非负整数上的m × n矩阵。A的隔离数是A中隔离项的最大数目。我们研究了在非负整数上保持矩阵隔离数的线性算子。我们得到当且仅当T是一个(P,Q)算子，即对于固定置换矩阵P和Q, T (a) = PAQ或，m = n, T (a) = PAtQ，对于任意mx n矩阵a, T (a) = PAQ，其中At为a的转置时，T是一个强保持隔离数k的线性算子。
{"title":"ISOLATION NUMBERS OF INTEGER MATRICES AND THEIR PRESERVERS","authors":"LeRoy B. Beasley, K.-T. Kang, S. Song","doi":"10.4134/BKMS.B180210","DOIUrl":"https://doi.org/10.4134/BKMS.B180210","url":null,"abstract":"Let A be an m × n matrix over nonnegative integers. The isolation number of A is the maximum number of isolated entries in A. We investigate linear operators that preserve the isolation number of matrices over nonnegative integers. We obtain that T is a linear operator that strongly preserve isolation number k for 1 ≤ k ≤ min{m,n} if and only if T is a (P,Q)-operator, that is, for fixed permutation matrices P and Q, T (A) = PAQ or, m = n and T (A) = PAtQ for any m× n matrix A, where At is the transpose of A.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"535-545"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70359262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.
{"title":"INFINITE HORIZON OPTIMAL CONTROL PROBLEMS OF BACKWARD STOCHASTIC DELAY DIFFERENTIAL EQUATIONS IN HILBERT SPACES","authors":"H. Liang, Jianjun Zhou","doi":"10.4134/BKMS.B190207","DOIUrl":"https://doi.org/10.4134/BKMS.B190207","url":null,"abstract":"This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"311-330"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：