Georgian Mathematical Journal最新文献

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Action of higher derivations on semiprime rings 高等派生对半元环的作用

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-06-25 DOI: 10.1515/gmj-2024-2026

Shakir Ali, Vaishali Varshney

Let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> {m,n} be the fixed positive integers and let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="script">ℛ</m:mi> </m:math> {mathcal{R}} be a ring. In 1978, Herstein proved that a 2-torsion free prime ring <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="script">ℛ</m:mi> </m:math> {mathcal{R}} is commutative if there is a nonzero derivation d of R such that <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mo stretchy="false">[</m:mo> <m:mrow> <m:mi>d</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>ϱ</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:mi>d</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>ξ</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">]</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {[d(varrho),d(xi)]=0} for all <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mi>ϱ</m:mi> <m:mo>,</m:mo> <m:mi>ξ</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mi>R</m:mi> </m:mrow> </m:math> {varrho,xiin R} . In this article, we study the above mentioned classical result for higher derivations and describe the structure of semiprime rings by using the invariance property of prime ideals under higher derivations. Precisely, apart from proving some other important results, we prove the following. Let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:msub> <m:mi>d</m:mi> <m:mi>i</m:mi> </m:msub> <m:mo stretchy="false">)</m:mo

设 m , n {m,n} 是固定的正整数，设 ℛ {mathcal{R}} 是一个环。1978 年，赫斯坦证明，如果 R 有一个非零派生 d，使得 [ d ( ϱ ) , d ( ξ ) ] = 0 {[d(varrho),d(xi)]=0} 对于所有 ϱ , ξ∈ R {varrho,xiin R} 而言，那么 2 个无扭素数环ℛ {mathcal{R}} 是交换环。 .在本文中，我们将研究上述关于高阶引申的经典结果，并利用素理想在高阶引申下的不变性来描述半素环的结构。确切地说，除了证明其他一些重要结果之外，我们还证明了以下内容。设 ( d i ) i∈ ℕ {(d_{i})_{iinmathbb{N}}} 和 ( g j ) j∈ ℕ {(g_{j})_{jinmathbb{N}}} 是半椭圆环 ℛ {mathcal{R}} 的两个高阶衍，使得 [ d n ( ϱ ) 、 g m ( ξ ) ] ∈ Z ( ℛ ) {[d_{n}(varrho),g_{m}(xi)]in Z(mathcal{R})} for all ϱ , ξ ∈ ℐ {varrho,xiinmathcal{I}} 其中ℐ {mathcal{I}} 是ℛ {mathcal{R}} 的理想。 .那么，要么ℛ {mathcal{R}} 是交换式的，要么 ( d i ) i∈ ℕ {(d_{i})_{iinmathbb{N}}} 的某个线性组合将 Z ( ℛ ) {Z(mathcal{R})} 为零，或者 ( g j ) j∈ ℕ {(g_{j})_{jinmathbb{N}} 的某个线性组合使 Z ( ℛ ) {Z(mathcal{R})} 为零。我们用实例来丰富我们的结果，证明其假设的必要性。最后，我们以进一步研究的方向结束本文。

引用次数: 0

Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations Dunkl 型 Segal-Bargmann 变换及其在某些偏微分方程中的应用

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-06-25 DOI: 10.1515/gmj-2024-2031

Fethi Soltani, Meriem Nenni

In this paper, we give some applications of the Dunkl-type Segal–Bargmann transform ℬ α

{mathscr{B}_{alpha}}

in the field of partial differential equations, such as the time-dependent Dunkl–Dirac Laplacian equation and the time-dependent Dunkl–Schrödinger equation. The resolution of these types of problems is based on the techniques of the transmutation operators on the Dunkl-type Fock space ℱ α ⁢ ( ℂ d )

{mathscr{F}_{alpha}(mathbb{C}^{d})}

本文给出了邓克尔型西格尔-巴格曼变换ℬ α {mathscr{B}_{alpha}} 在偏微分方程领域的一些应用，例如时变邓克尔-狄拉克拉普拉斯方程和时变邓克尔-薛定谔方程。这类问题的解决基于邓克尔型福克空间 ℱ α ( ℂ d ) {mathscr{F}_{alpha}(mathbb{C}^{d})} 上的嬗变算子技术。

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引用次数: 0

The influence of c-subnormality subgroups on the structure of finite groups c-subnormality 子群对有限群结构的影响

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-06-25 DOI: 10.1515/gmj-2024-2036

Dana Jaraden, Ali Ateiwi, Jehad Jaraden

Let H be a subgroup of a group G. We say that H is c-subnormal in G if there exists a subnormal subgroup T of G such that H ⁢ T = G

{HT=G}

and H ∩ T ⩽ H G

{Hcap Tleqslant H_{G}}

, where H G

{H_{G}}

is the maximal normal subgroup of G which is contained in H. In this paper, we investigate the structure of a finite group G under the assumption that all maximal subgroups are c-subnormal subgroups and present some new conditions for supersolvability.

如果存在一个 G 的子正则子群 T，使得 H T = G {HT=G}，并且 H ∩ T ⩽ H G {Hcap Tleqslant H_{G}} ，我们就说 H 在 G 中是 c 正则子群。本文研究了在所有最大子群都是 c-subnormal 子群的假设下有限群 G 的结构，并提出了一些新的超可溶条件。

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引用次数: 0

New estimates for the Berezin number of Hilbert space operators 希尔伯特空间算子贝雷津数的新估计值

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-03-25 DOI: 10.1515/gmj-2024-2012

Parvaneh Zolfaghari

In this article, we improve some Berezin number inequalities concerning a Hilbert space. It is shown that if T is a bounded linear operator on a Hilbert space, then for any <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>r</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {rgeq 1} , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>𝐛𝐞𝐫</m:mi> <m:mrow> <m:mn>2</m:mn> <m:mo>⁢</m:mo> <m:mi>r</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>T</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>≤</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> <m:msup> <m:mi>𝐛𝐞𝐫</m:mi> <m:mi>r</m:mi> </m:msup> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mo stretchy="false">|</m:mo> <m:msup> <m:mi>T</m:mi> <m:mo>*</m:mo> </m:msup> <m:msup> <m:mo stretchy="false">|</m:mo> <m:mrow> <m:mn>2</m:mn> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>-</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:msup> <m:mo stretchy="false">|</m:mo> <m:mi>T</m:mi> <m:msup> <m:mo stretchy="false">|</m:mo> <m:mrow> <m:mn>2</m:mn> <m:mo>⁢</m:mo> <m:mi>t</m:mi> </m:mrow> </m:msup> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:mn>4</m:mn> </m:mfrac> <m:mo>∥</m:mo> <m:mo stretchy="false">|</m:mo> <m:mi>T</m:mi> <m:msup> <m:mo stretchy="false">|</m:mo> <m:mrow> <m:mn>4</m:mn> <m:mo>⁢</m:mo> <m:mi>r</m:mi> <m:mo>⁢</m:mo> <m:mi>t</m:mi> </m:mrow> </m:msup> <m:mo>+</m:mo> <m:mo stretchy="false">|</m:mo> <m:msup> <m:mi>T</m:mi> <m:mo>*</m:mo> </m:msup> <m:msup> <m:mo stretchy="false">|</m:mo> <m:mrow> <m:mn>4</m:mn> <m:mo>⁢</m:mo> <m:mi>r</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>-</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:msup> <m:msub> <m:mo>∥</m:mo> <m:mi>𝐛𝐞𝐫</m:mi> </m:msub> <m:mo mathvariant="italic" separator="true"> </m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mn>0</m:mn> <m:mo>≤</m:mo> <m:mi>t</m:mi> <m:mo>≤</m:mo> <m:mn>1</m:mn> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:math> mathbf{ber}^{2r}(T)leqfrac{1}{2}mathbf{ber}^{r}({{|{{T}^{*}}|}^{2(1-t)}}{{% |T|}^{2t}})+frac{1}{4}{{|{{|T|}^{4rt}}+{{|{{T}^{*}}|}^{4r(1-t)}}|}_{mathbf% {ber}}}quad(0leq tleq 1), where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mo

在本文中，我们改进了一些关于希尔伯特空间的贝雷津数不等式。结果表明，如果 T 是希尔伯特空间上的有界线性算子，那么对于任意 r ≥ 1 {rgeq 1} ，𝐛𝐞𝐫𝐫是有界线性算子。 𝐛𝐞𝐫 2 r ( T ) ≤ 1 2 𝐛𝐞𝐫 r ( | T * | 2 ( 1 - t ) | T | 2 t ) + 1 4 ∥ | T | 4 r t + | T * | 4 r ( 1 - t ) ∥ 𝐛𝐞𝐫 ( 0 ≤ t ≤ 1 ) 、 mathbf{ber}^{2r}(T)leqfrac{1}{2}mathbf{ber}^{r}({{|{{T}^{*}}|}^{2(1-t)}}{{% |T|}^{2t}})+frac{1}{4}{{|{{|T|}^{4rt}}+{{|{{T}^{*}}|}^{4r(1-t)}}|}_{mathbf% {ber}}}quad(0leq tleq 1), 其中 | T | = ( T * T ) 1 2 {|T|={{({{T}^{*}}T)}^{frac{1}{2}}}} .

引用次数: 0

On generalized derivations in factor rings 论因子环中的广义推导

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-03-25 DOI: 10.1515/gmj-2024-2017

Mohammed Zerra, Karim Bouchannafa, Lahcen Oukhtite

The main purpose of this paper is to scrutinize the deportment of generalized derivations of R satisfying some functional *

{*}

-identities involving the center of the factor ring R / P

{R/P}

where P is a prime ideal of the ring R. Moreover, we suggest to give generalization of some well known results.

本文的主要目的是仔细研究满足某些函数 * {*} -identities 的 R 的广义派生的描述。 -此外，我们建议对一些众所周知的结果进行概括。

引用次数: 0

Group invertibility of the sum in rings and its applications 环中和的群可逆性及其应用

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-03-25 DOI: 10.1515/gmj-2024-2010

Huanyin Chen, Dayong Liu, Marjan Sheibani

We present necessary and sufficient conditions under which the sum of two group invertible elements in a ring is group invertible. As applications, we establish the existence of group inverses of certain 2 × 2

{2times 2}

block-operator matrices over a Banach space. These generalize the known results, e.g., Zhou, Chen and Zhu (Comm. Algebra 48 (2020), 676–690) and Benítez, Liu and Zhu (Linear Multilinear Algebra 59 (2011), 279–289).

我们提出了环中两个群可逆元素之和是群可逆的必要条件和充分条件。作为应用，我们建立了巴拿赫空间上某些 2 × 2 {2times 2} 块操作矩阵的群逆存在性。这些结果概括了已知结果，如 Zhou, Chen and Zhu (Comm.代数 48 (2020), 676-690) 和 Benítez、Liu 和 Zhu (Linear Multilinear Algebra 59 (2011), 279-289).

引用次数: 0

Generalized Stockwell transforms: Spherical mean operators and applications 广义斯托克韦尔变换球面均值算子及其应用

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-03-25 DOI: 10.1515/gmj-2024-2014

Saifallah Ghobber, Hatem Mejjaoli

The spherical mean operator has been widely studied and has seen remarkable development in many areas of harmonic analysis. In this paper, we consider the Stockwell transform related to the spherical mean operator. Since the study of time-frequency analysis is both theoretically interesting and practically useful, we will study several problems for the generalized Stockwell transform. Firstly, we explore the Shapiro uncertainty principle for this transformation. Next, we will study the boundedness and then the compactness of localization operators related to the generalized Stockwell transform, and finally we will introduce and study its scalogram.

球均值算子已被广泛研究，并在谐波分析的许多领域得到了显著发展。在本文中，我们将研究与球面均值算子相关的斯托克韦尔变换。由于时频分析的研究既有理论意义又有实用价值，我们将研究广义斯托克韦尔变换的几个问题。首先，我们将探讨该变换的沙皮罗不确定性原理。接着，我们将研究与广义斯托克韦尔变换相关的局部化算子的有界性和紧凑性，最后我们将介绍并研究其示意图。

引用次数: 0

Weak type estimates of genuine Calderón–Zygmund operators on the local Morrey spaces associated with ball quasi-Banach function spaces 与球准巴纳赫函数空间相关的局部莫雷空间上真正卡尔德龙-齐格蒙德算子的弱类型估计

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-03-25 DOI: 10.1515/gmj-2024-2013

Mingwei Shi, Jiang Zhou, Songbai Wang

Weak type estimates for genuine Calderón–Zygmund operators are established on the local Morrey spaces associated with ball quasi-Banach function spaces by two different methods. Above all, we obtain weak type estimates for the operator on the local weak Morrey spaces with variable exponents.

通过两种不同的方法，我们在与球准巴纳赫函数空间相关的局部莫雷空间上建立了真正卡尔德龙-齐格蒙德算子的弱类型估计。首先，我们在具有可变指数的局部弱莫里空间上获得了算子的弱类型估计。

引用次数: 0

σ-symmetric amenability of Banach algebras 巴拿赫代数的σ对称可亲和性

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-03-25 DOI: 10.1515/gmj-2024-2011

Lin Chen, Mohammad Javad Mehdipour, Jun Li

In this paper, we introduce the notion of σ-symmetric amenability of Banach algebras and investigate some hereditary properties of them. We also apply our results to several abstract Segal algebras and group algebras.

在本文中，我们介绍了巴拿赫代数的 σ 对称可亲性概念，并研究了它们的一些遗传性质。我们还将我们的结果应用于几个抽象的西格尔代数和群代数。

引用次数: 0

Constructions and characterizations of mixed reverse-order laws for the Moore–Penrose inverse and group inverse 摩尔-彭罗斯逆和群逆的混合逆序定律的构造和特征

IF 0.7 4区数学 Q2 MATHEMATICS

Georgian Mathematical Journal

Pub Date : 2024-03-25 DOI: 10.1515/gmj-2024-2016

Yongge Tian

This paper is concerned with constructions and characterizations of matrix equalities that involve mixed products of Moore–Penrose inverses and group inverses of two matrices. We first construct a mixed reverse-order law <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>A</m:mi> <m:mo>⁢</m:mo> <m:mi>B</m:mi> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>†</m:mo> </m:msup> <m:mo>=</m:mo> <m:mrow> <m:msup> <m:mi>B</m:mi> <m:mo>∗</m:mo> </m:msup> <m:mo>⁢</m:mo> <m:msup> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:msup> <m:mi>A</m:mi> <m:mo>∗</m:mo> </m:msup> <m:mo>⁢</m:mo> <m:mi>A</m:mi> <m:mo>⁢</m:mo> <m:mi>B</m:mi> <m:mo>⁢</m:mo> <m:msup> <m:mi>B</m:mi> <m:mo>∗</m:mo> </m:msup> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mi mathvariant="normal">#</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:msup> <m:mi>A</m:mi> <m:mo>∗</m:mo> </m:msup> </m:mrow> </m:mrow> </m:math> {(AB)^{{dagger}}=B^{ast}(A^{ast}ABB^{ast})^{#}A^{ast}} , and show that this matrix equality always holds through the use of a special matrix rank equality and some matrix range operations, where A and B are two matrices of appropriate sizes, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mo rspace="4.2pt" stretchy="false">(</m:mo> <m:mo rspace="4.2pt">⋅</m:mo> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>∗</m:mo> </m:msup> </m:math> {(,cdot,)^{ast}} , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mo rspace="4.2pt" stretchy="false">(</m:mo> <m:mo rspace="4.2pt">⋅</m:mo> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>†</m:mo> </m:msup> </m:math> {(,cdot,)^{{dagger}}} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mo rspace="4.2pt" stretchy="false">(</m:mo> <m:mo rspace="4.2pt">⋅</m:mo> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mi mathvariant="normal">#</m:mi> </m:msup> </m:math> {(,cdot,)^{#}} mean the conjugate transpose, the Moor

本文关注涉及两个矩阵的摩尔-彭罗斯倒数和群倒数的混合乘积的矩阵等式的构造和特征。我们首先构建了一个混合逆序律 ( A B ) † = B ∗ ( A ∗ A B B ∗ ) # A ∗ {(AB)^{{dagger}}=B^{ast}(A^{/ast}ABB^{/ast})^{#}A^{/ast}} ，并通过证明这个矩阵相等总是成立的，来说明这个矩阵相等是正确的。通过使用特殊的矩阵秩相等和一些矩阵范围运算，证明这个矩阵相等总是成立的，其中 A 和 B 是两个适当大小的矩阵，( ⋅ ) ∗ {(,cdot,)^{ast}} ，( ⋅ ) † {(,cdot,)^{ast}} 。 , ( ⋅ ) † {(cdot,)^{{dagger}} 和 ( ⋅ ) # {(cdot,)^{#}} 分别指矩阵的共轭转置、摩尔-彭罗斯逆和群逆。然后，我们给出了这一等式的各种变化形式，并推导出它们成立的必要条件和充分条件。特别是特别是，我们展示了一个有趣的事实，即两个反序规律( A B ) † = B † A † {(AB)^{{dagger}}=B^{{dagger}}A^{{dagger}}} 和 ( A ∗ A B B∗ ) # = ( B B ∗ ) # ( A A ) # {(A^{ast}ABB^{ast})^{#}=(BB^{ast})^{#}(A^{ast}A)^{#}} 是等价的。

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全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

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