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Archiv der Mathematik最新文献

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On the radical of group rings 在基团环的根上
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-07 DOI: 10.1007/s00013-025-02208-9
F. E. A. Johnson
{"title":"On the radical of group rings","authors":"F. E. A. Johnson","doi":"10.1007/s00013-025-02208-9","DOIUrl":"10.1007/s00013-025-02208-9","url":null,"abstract":"<div><p>It is conjectured that, for any group <i>G</i>, the Jacobson radical <span>(J({mathbb {Z}}[G]))</span> of the integral group ring <span>({mathbb {Z}}[G])</span> is zero. This is known to be true when <i>G</i> is finite. Here we show it is true for a reasonably large class of infinite groups, including finitely generated linear groups and groups which satisfy Higman’s ‘two unique products’ condition.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"239 - 246"},"PeriodicalIF":0.5,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02208-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On extensions of principal series representations 关于主级数表示的扩展
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-06 DOI: 10.1007/s00013-025-02210-1
Gautam H. Borisagar, Asfak Soneji
{"title":"On extensions of principal series representations","authors":"Gautam H. Borisagar,&nbsp;Asfak Soneji","doi":"10.1007/s00013-025-02210-1","DOIUrl":"10.1007/s00013-025-02210-1","url":null,"abstract":"<div><p>We compute <span>(textrm{Ext}^{1}_B(chi _1,chi _2))</span> between two characters <span>(chi _1,chi _2)</span> of a Borel subgroup <i>B</i> of a split reductive group <i>G</i> over a finite field <span>(mathbb {F}_q,)</span> and make an application to the calculation of <span>(textrm{Ext}^1_G(pi _1,pi _2))</span> between principal series representations <span>(pi _1,pi _2)</span> of <span>(G(mathbb {F}_q))</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"121 - 126"},"PeriodicalIF":0.5,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337750","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}
引用次数: 0
Answer to a question of Hung and Tiep on conductors of cyclotomic integers 关于环切整数导体的Hung和Tiep问题的回答
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-06 DOI: 10.1007/s00013-025-02212-z
Christopher Herbig
{"title":"Answer to a question of Hung and Tiep on conductors of cyclotomic integers","authors":"Christopher Herbig","doi":"10.1007/s00013-025-02212-z","DOIUrl":"10.1007/s00013-025-02212-z","url":null,"abstract":"<div><p>In Question 5.2, Hung and Tiep (Eur J Math 9, 2023) asked the following: If <span>(alpha )</span> is a sum of <i>k</i> complex roots of unity and <span>(mathbb {Q}_{c(alpha )})</span> is the smallest cyclotomic field containing <span>(alpha )</span>, is it true that <span>(|mathbb {Q}_{c(alpha )}:mathbb {Q}(alpha )| le k)</span>? We answer this question in the negative, and in §4, we shall bound the growth of <span>(|mathbb {Q}_{c(alpha )}:mathbb {Q}(alpha )|)</span> as a function of <i>k</i> using known results on minimal vanishing sums.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"247 - 256"},"PeriodicalIF":0.5,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337751","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}
引用次数: 0
On the invertibility of bounded operators with a lower bound on reflexive Banach spaces, and applications to (C_{0})-semigroups 自反Banach空间上有下界算子的可逆性及其在(C_{0}) -半群上的应用
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-04 DOI: 10.1007/s00013-025-02209-8
Belabbas Madani
{"title":"On the invertibility of bounded operators with a lower bound on reflexive Banach spaces, and applications to (C_{0})-semigroups","authors":"Belabbas Madani","doi":"10.1007/s00013-025-02209-8","DOIUrl":"10.1007/s00013-025-02209-8","url":null,"abstract":"<div><p>We present a new version of an invertibility result for operators satisfying a lower bound condition. The result states that any bounded operator on a reflexive Banach space, which satisfies the lower bound condition, can be extended to a larger reflexive Banach space where it becomes invertible. Furthermore, we provide applications to <span>(C_{0})</span>-semigroups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"305 - 313"},"PeriodicalIF":0.5,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337118","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}
引用次数: 0
Newly appointed editors 新任命的编辑
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-12-05 DOI: 10.1007/s00013-025-02203-0
{"title":"Newly appointed editors","authors":"","doi":"10.1007/s00013-025-02203-0","DOIUrl":"10.1007/s00013-025-02203-0","url":null,"abstract":"","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"1 - 1"},"PeriodicalIF":0.5,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969465","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}
引用次数: 0
Local (L^2)-boundedness of rough Fourier integral operators with the rough corank condition 粗糙corank条件下粗糙傅立叶积分算子的局部(L^2)有界性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-12-05 DOI: 10.1007/s00013-025-02207-w
Xiao Yu, Xiangrong Zhu
{"title":"Local (L^2)-boundedness of rough Fourier integral operators with the rough corank condition","authors":"Xiao Yu,&nbsp;Xiangrong Zhu","doi":"10.1007/s00013-025-02207-w","DOIUrl":"10.1007/s00013-025-02207-w","url":null,"abstract":"<div><p>In this paper, we consider a rough Fourier integral operator defined as </p><div><div><span>$$T_{phi ,a}f(x)=int limits _{mathbb {R}^{n}}e^{iphi (x,xi )}a(x,xi )hat{f}(xi )dxi ,$$</span></div></div><p>where the amplitude <span>(ain L^{infty }S^{m}_{rho })</span> and the phase <span>(phi in L^{infty }Phi ^{2})</span> satisfy the rough <i>k</i>-corank condition. The motivation for this problem stems from the regularity of the maximal wave operator. We prove that this operator is bounded from <span>(L^{2})</span> to <span>(L_{text {loc}}^{2})</span> provided </p><div><div><span>$$m&lt;min left{ frac{n(rho -1)}{2},frac{rho }{2}-frac{n+1}{4}right} -frac{krho }{2}.$$</span></div></div></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"315 - 327"},"PeriodicalIF":0.5,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337028","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}
引用次数: 0
Image ratios of word maps and polynomial maps 词映射和多项式映射的图像比率
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-12-03 DOI: 10.1007/s00013-025-02194-y
Saikat Panja
{"title":"Image ratios of word maps and polynomial maps","authors":"Saikat Panja","doi":"10.1007/s00013-025-02194-y","DOIUrl":"10.1007/s00013-025-02194-y","url":null,"abstract":"<div><p>Let <i>A</i> be a finite group (or a finite algebra), and <span>(omega )</span> be a word map (resp. polynomial map) on <i>n</i> many generators. We define the quantity <span>(|omega (A)|/|A|)</span> as the <i>image ratio of</i> <span>(omega )</span> <i>on</i> <i>A</i> and denote it by <span>(mu (omega ,A))</span>. In this article, we investigate the set <span>(textrm{R}(omega )={mu (omega , A) : A {text { is a finite group}}})</span>, and study the same for the case of rings. We demonstrate the existence of word maps whose set of image ratios is dense in [0, 1] for groups (and rings).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"21 - 28"},"PeriodicalIF":0.5,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969471","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}
引用次数: 0
A note on singularity indices of hyperelliptic fibrations 关于超椭圆型颤振奇异指数的一个注记
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-12-01 DOI: 10.1007/s00013-025-02198-8
Cheng Gong, Zhiming Guo, Xin Lü
{"title":"A note on singularity indices of hyperelliptic fibrations","authors":"Cheng Gong,&nbsp;Zhiming Guo,&nbsp;Xin Lü","doi":"10.1007/s00013-025-02198-8","DOIUrl":"10.1007/s00013-025-02198-8","url":null,"abstract":"<div><p>Let <span>(f: X rightarrow B)</span> be a relatively minimal hyperelliptic fibration of genus <i>g</i>. For such a fibration <i>f</i>, Xiao introduced a series of singularity indices <span>(s_i(f))</span> for <span>(2le i le g+2)</span>. These indices provide an effective way to study the geometry of <i>f</i>. It is known that <span>(s_i(f)ge 0)</span> for <span>(ige 3)</span>, but it is not clear whether <span>(s_2(f))</span> is non-negative. In this note, we construct a sequence of hyperelliptic fibrations with <span>(s_2(f)&lt;0)</span>, where the genus <i>g</i> can be arbitrarily large.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"153 - 163"},"PeriodicalIF":0.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147335971","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}
引用次数: 0
Tor algebra of local rings with decomposable maximal ideal 具有可分解极大理想的局部环的托代数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-27 DOI: 10.1007/s00013-025-02200-3
Saeed Nasseh, Maiko Ono, Yuji Yoshino
{"title":"Tor algebra of local rings with decomposable maximal ideal","authors":"Saeed Nasseh,&nbsp;Maiko Ono,&nbsp;Yuji Yoshino","doi":"10.1007/s00013-025-02200-3","DOIUrl":"10.1007/s00013-025-02200-3","url":null,"abstract":"<div><p>Let <span>((R,mathfrak {m}_R))</span> be a commutative noetherian local ring. Assuming that <span>(mathfrak {m}_R=Ioplus J)</span> is a direct sum decomposition, where <i>I</i> and <i>J</i> are non-zero ideals of <i>R</i>, we describe the structure of the Tor algebra of <i>R</i> in terms of the Tor algebras of the rings <i>R</i>/<i>I</i> and <i>R</i>/<i>J</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"127 - 137"},"PeriodicalIF":0.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342384","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}
引用次数: 0
Concentration of norms of random vectors with independent p-sub-exponential coordinates 具有独立p次指数坐标的随机向量的规范集中
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-27 DOI: 10.1007/s00013-025-02199-7
Krzysztof Zajkowski
{"title":"Concentration of norms of random vectors with independent p-sub-exponential coordinates","authors":"Krzysztof Zajkowski","doi":"10.1007/s00013-025-02199-7","DOIUrl":"10.1007/s00013-025-02199-7","url":null,"abstract":"<div><p>We present examples of <i>p</i>-sub-exponential random variables for any positive <i>p</i>. We prove two types of concentration of standard <i>p</i>-norms (2-norm is the Euclidean norm) of random vectors with independent <i>p</i>-sub-exponential coordinates around the Lebesgue <span>(L^p)</span>-norms of these <i>p</i>-norms of random vectors. In the first case <span>(pge 1)</span>, our estimates depend on the dimension <i>n</i> of random vectors. But in the second one for <span>(pge 2)</span>, with an additional assumption, we get an estimate that does not depend on <i>n</i>. In other words, we generalize some known concentration results in the Euclidean case to cases of the <i>p</i>-norms of random vectors with independent <i>p</i>-sub-exponential coordinates.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"209 - 220"},"PeriodicalIF":0.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02199-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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