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Free g-dimonoids are determined by their endomorphism semigroups 自由g-二精是由它们的自同态半群决定的
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-09-22 DOI: 10.1007/s00013-026-02280-9
Anatolii V. Zhuchok, Yuliia V. Zhuchok
{"title":"Free g-dimonoids are determined by their endomorphism semigroups","authors":"Anatolii V. Zhuchok,&nbsp;Yuliia V. Zhuchok","doi":"10.1007/s00013-026-02280-9","DOIUrl":"10.1007/s00013-026-02280-9","url":null,"abstract":"<div><p>The problem of determinability for free algebras in a given variety was formulated by B.I. Plotkin in his lectures on universal algebraic geometry. It was solved for free groups by E. Formanek, and for free semigroups and free monoids by G. Mashevitsky and B.M. Schein. We solve the determinability problem for free <i>g</i>-dimonoids which generalize free semigroups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 3","pages":"233 - 240"},"PeriodicalIF":0.6,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02280-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149078827","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
A conjecture on the Schauder fixed point theorem and the degree of non-densifiability 关于Schauder不动点定理和非致密度的一个猜想
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-09-16 DOI: 10.1007/s00013-026-02283-6
Gonzalo García
{"title":"A conjecture on the Schauder fixed point theorem and the degree of non-densifiability","authors":"Gonzalo García","doi":"10.1007/s00013-026-02283-6","DOIUrl":"10.1007/s00013-026-02283-6","url":null,"abstract":"<div><p>We revisit a conjecture posed in 1972 by Nussbaum on a generalization of the Schauder fixed point theorem. Instead of requiring compactness of iterates, we introduce the notion of <i>n</i>-DND-condensing mappings, based on the degree of non-densifiability (DND). Roughly speaking, the DND measures, in the specified sense, the distance from a bounded subset of a metric space to the class of Peano continua contained in it. Our main result shows that under suitable additional conditions such mappings have a fixed point. Also, through some examples, we show that the new result works in cases where other known results do not.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 3","pages":"295 - 304"},"PeriodicalIF":0.6,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149078829","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 a class of abelian groups with sufficiently many T-sequences 一类具有足够多t序列的阿贝尔群
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-09-12 DOI: 10.1007/s00013-026-02282-7
D. Dikranjan, A. Giordano Bruno
{"title":"On a class of abelian groups with sufficiently many T-sequences","authors":"D. Dikranjan,&nbsp;A. Giordano Bruno","doi":"10.1007/s00013-026-02282-7","DOIUrl":"10.1007/s00013-026-02282-7","url":null,"abstract":"<div><p>We describe the one-to-one sequences <span>(textbf{u})</span> in an abelian group <i>G</i> that have a <i>T</i>-subsequence, and we show that they are the same as those that admit a <i>TB</i>-subsequence. In terms of the Zariski topology, these are precisely the sequences <span>(textbf{u})</span> such that 0 belongs to the Zariski closure of the supporting set of <span>(textbf{u})</span>. Additionally, we extend this result to <span>(T^mathcal {I})</span>- and <span>(TB^mathcal {I})</span>-subsequences defined using <span>(mathcal {I})</span>-convergence where <span>(mathcal {I})</span> is an ideal of <span>(mathbb {N}_0)</span>. As a corollary, we describe completely the class <span>(mathfrak T)</span> (resp., <span>(mathfrak T_B)</span>, <span>(mathfrak T^mathcal {I})</span>, <span>(mathfrak T_B^mathcal {I})</span>) of abelian groups in which every one-to-one sequence has a <i>T</i>-subsequence (resp., <i>TB</i>-, <span>(T^mathcal {I})</span>-, <span>(TB^mathcal {I})</span>-subsequence). These are precisely the abelian groups that are either almost torsion-free or of prime exponent, in other words, the groups with cofinite Zariski topology [5].</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 3","pages":"215 - 232"},"PeriodicalIF":0.6,"publicationDate":"2026-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02282-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149078835","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
Small Pisot type generators of number fields 数字字段的小型Pisot类型生成器
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-09-12 DOI: 10.1007/s00013-026-02287-2
Artūras Dubickas
{"title":"Small Pisot type generators of number fields","authors":"Artūras Dubickas","doi":"10.1007/s00013-026-02287-2","DOIUrl":"10.1007/s00013-026-02287-2","url":null,"abstract":"<div><p>In this paper, we show that each number field <i>K</i> contains a small Pisot number (real or complex) that generates the field <i>K</i>. For example, each complex field <i>K</i> of degree <i>d</i> over <span>({mathbb {Q}})</span>, except for some totally complex fields <i>K</i>, has a complex Pisot generator <span>(alpha )</span> satisfying <span>(|alpha |ll _d |Delta _K|^{1/4})</span>, where <span>(Delta _K)</span> is the discriminant of <i>K</i>. We also give a new lower bound on Mahler’s measure of a unit generator <span>(alpha )</span> of <i>K</i> in terms of <span>(Delta _K)</span>. If <i>K</i> of degree <span>(d ge 2)</span> has exactly one real embedding, then the Mahler measure <span>(M(alpha ))</span> of its unit generator <span>(alpha )</span> is always at least <span>(d^{-d/(2d-3)}|Delta _K|^{1/(2d-3)}.)</span></p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 3","pages":"273 - 284"},"PeriodicalIF":0.6,"publicationDate":"2026-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149078834","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 vanishing of ({{textsf{Ext}}}) and ({textsf{Tor}}) 关于({{textsf{Ext}}})和的消失 ({textsf{Tor}})
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-08-29 DOI: 10.1007/s00013-026-02274-7
Abdolnaser Bahlekeh, Shokrollah Salarian
{"title":"On the vanishing of ({{textsf{Ext}}}) and ({textsf{Tor}})","authors":"Abdolnaser Bahlekeh,&nbsp;Shokrollah Salarian","doi":"10.1007/s00013-026-02274-7","DOIUrl":"10.1007/s00013-026-02274-7","url":null,"abstract":"<div><p>This paper contains two theorems concerning the vanishing of natural transformations of (co)homology functors. Precisely, assume that <i>R</i> is an associative ring with identity and <span>(f: Mrightarrow N)</span> is a morphism of finitely presented right <i>R</i>-modules. The first theorem proves that the natural transformation <span>({{textsf{Ext}}}^1(f, -))</span> vanishes over the category of all right <i>R</i>-modules if and only if <span>({textsf{Tor}}_1(f, -))</span> vanishes over the category of all left <i>R</i>-modules. As a corollary of this result, we establish that <span>({{textsf{Ext}}}^1(f, -))</span> is epic if and only if <span>({textsf{Tor}}_1(f, -))</span> is monic. The second theorem shows that if <i>R</i> is left and right Noetherian and <i>M</i>, <i>N</i> are Gorenstein projective, then the natural transformations <span>({textsf{Tor}}_1(f, -))</span>, <span>({{textsf{Ext}}}^1(-, f))</span>, and <span>({{textsf{Ext}}}^1(f, -))</span> vanish over the category of all Gorenstein projective modules, simultaneously. This, in particular, yields that over Gorenstein projective modules, the notions of phantom morphisms and <span>({{textsf{Ext}}})</span>-phantom morphisms coincide. Also, it is proved that if <i>R</i> is <i>n</i>-Gorenstein, then for any integer <span>(i&gt;n)</span>, the natural transformations <span>({{textsf{Ext}}}^{i}(f, -))</span>, <span>({{textsf{Ext}}}^{i}(-, f))</span>, and <span>({textsf{Tor}}_{i}(f, -))</span> vanish over all modules, simultaneously. As an interesting consequence, we show that under the same assumptions, <span>({{textsf{Ext}}}^i(-, f))</span> is epic (resp. monic) if and only if <span>({{textsf{Ext}}}^i(f, -))</span> is monic (resp. epic) if and only if <span>({textsf{Tor}}_i(f, -))</span> is epic (resp. monic).\u0000</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 3","pages":"241 - 254"},"PeriodicalIF":0.6,"publicationDate":"2026-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149078837","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
Metric Poissonian pair correlation ansssssd additive energy 度量泊松对相关分析加性能量
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-08-29 DOI: 10.1007/s00013-026-02277-4
Tanmoy Bera, E. Malavika
{"title":"Metric Poissonian pair correlation ansssssd additive energy","authors":"Tanmoy Bera,&nbsp;E. Malavika","doi":"10.1007/s00013-026-02277-4","DOIUrl":"10.1007/s00013-026-02277-4","url":null,"abstract":"<div><p>In this article, we prove that for a strictly increasing sequence <span>((a_n))</span> of natural numbers, if the additive energy of <span>({a_n:nle N})</span> is less than <span>(N^3/(log N)^C)</span> for some <span>(Cge 14.71,)</span> then <span>(({a_nalpha }))</span> has Poissonian pair correlation for almost all <span>(alpha in mathbb {R}.)</span> This provides a lower bound for the exponent <i>C</i> in the additive energy bound established by Bloom and Walker [4].</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 3","pages":"285 - 294"},"PeriodicalIF":0.6,"publicationDate":"2026-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149078828","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 fixed point approach to non-commutative central limit theorems 非交换中心极限定理的不动点逼近
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-08-25 DOI: 10.1007/s00013-026-02271-w
Jad Hamdan
{"title":"A fixed point approach to non-commutative central limit theorems","authors":"Jad Hamdan","doi":"10.1007/s00013-026-02271-w","DOIUrl":"10.1007/s00013-026-02271-w","url":null,"abstract":"<div><p>We show how the renormalization group approach can be used to prove quantitative central limit theorems (CLTs) in the setting of free, Boolean, bi-free, and bi-Boolean independence under finite third moment assumptions. The proofs rely on the construction of a contraction on a subspace of probability measures over <span>(mathbb {R})</span> (or <span>(mathbb {R}^2)</span>) equipped with a suitable metric, which has the appropriate analogue of a Gaussian distribution as a fixed point (for instance, the semi-circle law in the case of free independence). In all cases, this yields a convergence rate of <span>(1/sqrt{n})</span>, and we show that this can be improved to 1/<i>n</i> in some instances under stronger assumptions.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 3","pages":"305 - 321"},"PeriodicalIF":0.6,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02271-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149078838","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
A reciprocity theorem of Robinson–Benson–Webb for finite-dimensional symmetric algebras 有限维对称代数的Robinson-Benson-Webb互易定理
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-08-25 DOI: 10.1007/s00013-026-02281-8
Shigeo Koshitani
{"title":"A reciprocity theorem of Robinson–Benson–Webb for finite-dimensional symmetric algebras","authors":"Shigeo Koshitani","doi":"10.1007/s00013-026-02281-8","DOIUrl":"10.1007/s00013-026-02281-8","url":null,"abstract":"<div><p>We extend the reciprocity theorem of G.R. Robinson, D. Benson and P. Webb, between a finite group and its subgroup to the case of finite-dimensional <i>symmetric</i> algebras over a field which are connected by a bimodule for the two algebras.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 3","pages":"255 - 259"},"PeriodicalIF":0.6,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149078836","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 twisted Edwards curve over a local ring 一个局部环上扭曲的爱德华兹曲线
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-08-11 DOI: 10.1007/s00013-026-02276-5
Abdelhakim Chillali, Moha Ben Taleb El Hamam, Abdelâli Grini
{"title":"A twisted Edwards curve over a local ring","authors":"Abdelhakim Chillali,&nbsp;Moha Ben Taleb El Hamam,&nbsp;Abdelâli Grini","doi":"10.1007/s00013-026-02276-5","DOIUrl":"10.1007/s00013-026-02276-5","url":null,"abstract":"<div><p>Let <i>q</i> be an odd prime power and consider the local ring <span>(A_3:= {mathbb {F}_{q}[X]}/{X^{3}})</span>, where <span>(mathbb {F}_{q})</span> is the field of <i>q</i> elements. Let <span>(E_{E_{a,d}}(A_3))</span> denote the twisted Edwards curves over <span>(A_3)</span>. The purpose of this paper is to investigate the properties of <span>(E_{E_{a,d}}(A_3))</span> and equip it with a new group structure. This new group structure on <span>(E_{E_{a,d}}(A_3))</span> leads to an isomorphism between <span>(E_{E_{a,d}}(A_3))</span> and <span>(E_{E_{a_{0},d_{0}}}times mathbb {F}_{q}^2)</span>, where <span>(E_{E_{a_{0},d_{0}}})</span> is the twisted Edwards curve over <span>(mathbb {F}_{q})</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 3","pages":"261 - 271"},"PeriodicalIF":0.6,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149078830","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 sum of a prime and a number that is not square-free 一个质数和一个非平方数的和
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-08-05 DOI: 10.1007/s00013-026-02275-6
Ethan Simpson Lee, Rowan O’Clarey
{"title":"On the sum of a prime and a number that is not square-free","authors":"Ethan Simpson Lee,&nbsp;Rowan O’Clarey","doi":"10.1007/s00013-026-02275-6","DOIUrl":"10.1007/s00013-026-02275-6","url":null,"abstract":"<div><p>We prove that every sufficiently large integer <i>n</i> can be written as the sum of a prime and an integer that is not square-free. In addition, we expect this result holds for every <span>(n &gt; 24)</span> and prove two results to support this claim. First, we prove the result holds unconditionally for every odd <span>(n &gt; 24)</span>. Second, assuming the Generalised Riemann Hypothesis for Dirichlet <i>L</i>-functions, we prove the result holds for every <span>(n &gt; 24)</span>. We also discuss the obstruction which prohibits us from proving the result unconditionally for every <span>(n &gt; 24)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"127 2","pages":"153 - 163"},"PeriodicalIF":0.6,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02275-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719146","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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