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Functors for Long dimodules and Yetter–Drinfeld modules in a weak setting 弱设置下长模和叶氏模的函子
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-03-02 DOI: 10.4171/rsmup/125
J. Álvarez, R. G. Rodríguez
{"title":"Functors for Long dimodules and Yetter–Drinfeld modules in a weak setting","authors":"J. Álvarez, R. G. Rodríguez","doi":"10.4171/rsmup/125","DOIUrl":"https://doi.org/10.4171/rsmup/125","url":null,"abstract":"In this paper, for two weak Hopf monoids H and B with invertible antipode, we define a functor between the category of left-leftH⊗B-Yetter-Drinfeld modules and the one of H-B-Long dimodules. We also show that, if moreover H is quasitriangular and B is coquasitriangular, this functor is a retraction of the well-known injective functor between left-left H-B-Long dimodules and left-left H ⊗B-Yetter-Drinfeld modules. Mathematics Subject Classification (2020). Primary: 16T05; Secondary: 18M05, 18M15, 16T25.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"560 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85725638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytic general solutions of nonlinear second-order $q$-difference equations with a double characteristic value 具有双重特征值的非线性二阶q差分方程的解析通解
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-02-20 DOI: 10.4171/rsmup/89
Mami Suzuki
{"title":"Analytic general solutions of nonlinear second-order $q$-difference equations with a double characteristic value","authors":"Mami Suzuki","doi":"10.4171/rsmup/89","DOIUrl":"https://doi.org/10.4171/rsmup/89","url":null,"abstract":"As far as the author knows it seems that an existence theorem of a solution of a general nonlinear q-difference equation is not known. In this paper we will investigate a nonlinear second order q-difference equation whose characteristic equation has only one solution and will show analytic general solutions of such an equation. Further we will show an example. Mathematics Subject Classification (2010). Primary: 39A13; Secondary: 39A45.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88937555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Height pairings of 1-motives 1-动机的高度配对
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-02-03 DOI: 10.4171/rsmup/116
Carolina Rivera Arredondo
{"title":"Height pairings of 1-motives","authors":"Carolina Rivera Arredondo","doi":"10.4171/rsmup/116","DOIUrl":"https://doi.org/10.4171/rsmup/116","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80054881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Utumi Abelian groups Utumi阿贝尔群
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-02-03 DOI: 10.4171/rsmup/126
G. Călugăreanu, Soumitra Das
{"title":"Utumi Abelian groups","authors":"G. Călugăreanu, Soumitra Das","doi":"10.4171/rsmup/126","DOIUrl":"https://doi.org/10.4171/rsmup/126","url":null,"abstract":"In a recent paper written by Y. Ibrahim and M. Yousif (Comm. in Algebra, 2018), the following class of modules is considered: a right R-module M is called a Utumi module if, whenever A and B are submodules of M with A ∼= B and A∩B = 0, there exist direct summands K and L of M such that A is essential in K, B is essential in L and K ⊕ L is a direct summand of M . In this paper, all the Utumi Z-modules (i.e. Abelian groups) and some special classes of these are determined. As an application, it is proved that all the pseudo-continuous Abelian groups are quasi-continuous. Mathematics Subject Classification (2020).Primary: 20K21; Secondary: 20K30, 16D10.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81200585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weakly $S$-semipermutable subgroups and $p$-nilpotency of groups 群的弱$S$-半置换子群和$p$-幂零性
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-01-26 DOI: 10.4171/rsmup/112
Hassan Jafarian Dehkordy, G. Rezaeezadeh
{"title":"Weakly $S$-semipermutable subgroups and $p$-nilpotency of groups","authors":"Hassan Jafarian Dehkordy, G. Rezaeezadeh","doi":"10.4171/rsmup/112","DOIUrl":"https://doi.org/10.4171/rsmup/112","url":null,"abstract":"A subgroup H of a finite group G is said to be S-semipermutable in G if HGp = GpH for every Sylow subgroup Gp of G with (|H|, p) = 1. A subgroup H of G is said to be Weakly S-semipermutable in G if there exists a normal subgroup T of G such that HT is S-permutable and H ∩ T is S-semipermutable in G. In this paper we prove that for a finite group G, if some cyclic subgroups or maximal subgroups of G are Weakly S-semipermutable in G, then G is p-nilpotent. Mathematics Subject Classification (2010). Primary: 20D15; Secondary: 20D20, 20F19, 20D10.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79037953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Canonical universal locally finite groups 正则泛局部有限群
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-01-26 DOI: 10.4171/rsmup/117
S. Shelah
{"title":"Canonical universal locally finite groups","authors":"S. Shelah","doi":"10.4171/rsmup/117","DOIUrl":"https://doi.org/10.4171/rsmup/117","url":null,"abstract":"We prove that for lambda = beta_omega or just lambda strong limit singular of cofinality aleph_0, if there is a universal member in the class K^lf_lambda of locally finite groups of cardinality lambda, then there is a canonical one (parallel to special models for elementary classes, which is the replacement of universal homogeneous ones and saturated ones in cardinals lambda = lambda^<lambda). For this, we rely on the existence of enough indecomposable such groups, as proved in\"Density of indecomposable locally finite groups\". We also more generally deal with the existence of universal members in general classes for such cardinals.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"101 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77324872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A short proof of a non-vanishing result by Conca, Krattenthaler and Watanabe Conca, Krattenthaler和Watanabe对非消失结果的简短证明
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-01-13 DOI: 10.4171/rsmup/113
A. Bostan
{"title":"A short proof of a non-vanishing result by Conca, Krattenthaler and Watanabe","authors":"A. Bostan","doi":"10.4171/rsmup/113","DOIUrl":"https://doi.org/10.4171/rsmup/113","url":null,"abstract":"– In this note, we propose a short and elementary proof of a non-vanishing result by Conca, Krattenthaler and Watanabe (2009).","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83519289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Residual supersingular Iwasawa theory and signed Iwasawa invariants 残差超奇异Iwasawa理论与有符号Iwasawa不变量
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-01-11 DOI: 10.4171/rsmup/111
Filippo A. E. Nuccio Mortarino Majno di Capriglio, Sujatha Ramdorai
{"title":"Residual supersingular Iwasawa theory and signed Iwasawa invariants","authors":"Filippo A. E. Nuccio Mortarino Majno di Capriglio, Sujatha Ramdorai","doi":"10.4171/rsmup/111","DOIUrl":"https://doi.org/10.4171/rsmup/111","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77408247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Refined Kolmogorov inequalities for the binomial distribution 二项分布的改进Kolmogorov不等式
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-01-11 DOI: 10.4171/rsmup/115
R. Giuliano Antonini, V. Kruglov, Andrei Volodin
{"title":"Refined Kolmogorov inequalities for the binomial distribution","authors":"R. Giuliano Antonini, V. Kruglov, Andrei Volodin","doi":"10.4171/rsmup/115","DOIUrl":"https://doi.org/10.4171/rsmup/115","url":null,"abstract":"This paper presents refined versions of the well known Kolmogorov maximal inequality for the binomial distribution. Mathematics Subject Classification (2020). Primary: 60F10; Secondary: 60F15","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"59 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91400688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 extension of even families of non-congruent numbers 关于非同余数的偶族的扩展
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2022-12-20 DOI: 10.4171/rsmup/105
L. Reinholz, Qiduan Yang
{"title":"On the extension of even families of non-congruent numbers","authors":"L. Reinholz, Qiduan Yang","doi":"10.4171/rsmup/105","DOIUrl":"https://doi.org/10.4171/rsmup/105","url":null,"abstract":"A method that extends existing families of even non-congruent numbers to produce new families of non-congruent numbers with arbitrarily many distinct prime factors is presented. We show that infinitely many new non-congruent numbers can be generated by appending a suitable collection of primes onto any even non-congruent number whose corresponding congruent number elliptic curve has 2-Selmer rank of zero. Our method relies upon Monsky’s formula for computing the 2-Selmer rank of the congruent number elliptic curve. Even non-congruent numbers constructed according to our result have an unlimited number of prime factors in each odd congruence class modulo eight, and have congruent number elliptic curves with 2-Selmer rank equal to zero. Mathematics Subject Classification (2020). Primary: 11G05.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"101 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77901067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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