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.
{"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}
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.
{"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}
{"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}
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.
{"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}
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.
{"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}
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^
{"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}
{"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}
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}
This paper presents refined versions of the well known Kolmogorov maximal inequality for the binomial distribution. Mathematics Subject Classification (2020). Primary: 60F10; Secondary: 60F15
{"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}
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.
{"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}
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：