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Topological Algebra and its Applications最新文献

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On the relation between length functions and exact Sylvester rank functions 关于长度函数与精确Sylvester秩函数的关系
Topological Algebra and its Applications Pub Date : 2019-01-01 DOI: 10.1515/taa-2019-0006
Simone Virili
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引用次数: 4
Topological and metric entropy for group and semigroup actions 群和半群作用的拓扑熵和度量熵
Topological Algebra and its Applications Pub Date : 2019-01-01 DOI: 10.1515/taa-2019-0004
L. Stoyanov
{"title":"Topological and metric entropy for group and semigroup actions","authors":"L. Stoyanov","doi":"10.1515/taa-2019-0004","DOIUrl":"https://doi.org/10.1515/taa-2019-0004","url":null,"abstract":"Abstract It is well-known that the classical definition of topological entropy for group and semigroup actions is frequently zero in some rather interesting situations, e.g. smooth actions of ℤk+ (k >1) on manifolds. Different definitions have been considered by several authors. In the present article we describe the one proposed in 1995 by K.H.Hofmann and the author which produces topological entropy not trivially zero for such smooth actions. We discuss this particular approach, and also some of the main properties of the topological entropy defined in this way, its advantages and disadvantages compared with the classical definition. We also discuss some recent results, obtained jointly with Andrzej Biś, Dikran Dikranjan and Anna Giordano Bruno, of a similar definition of metric entropy, i.e. entropy with respect to an invariant measure for a group or a semigroup action, and some of its properties.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"7 1","pages":"38 - 47"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2019-0004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41477075","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: 1
A criterion of the existence of an embedding of a monothetic monoid into a topological group 一元一元群嵌入拓扑群的存在性准则
Topological Algebra and its Applications Pub Date : 2019-01-01 DOI: 10.1515/taa-2019-0001
B. Averbukh
{"title":"A criterion of the existence of an embedding of a monothetic monoid into a topological group","authors":"B. Averbukh","doi":"10.1515/taa-2019-0001","DOIUrl":"https://doi.org/10.1515/taa-2019-0001","url":null,"abstract":"Abstract Using properties of unitary Cauchy filters on monothetic monoids, we prove a criterion of the existence of an embedding of such a monoid into a topological group. The proof of the sufficiency is constructive: under the corresponding assumptions, we are building a dense embedding of a given monothetic monoid into a monothetic group.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"7 1","pages":"1 - 12"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2019-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45391489","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: 2
Localization of the Chain Recurrent set using Shape theory and Symbolical Dynamics 基于形状理论和符号动力学的链递归集的局部化
Topological Algebra and its Applications Pub Date : 2019-01-01 DOI: 10.1515/taa-2019-0002
M. Shoptrajanov
{"title":"Localization of the Chain Recurrent set using Shape theory and Symbolical Dynamics","authors":"M. Shoptrajanov","doi":"10.1515/taa-2019-0002","DOIUrl":"https://doi.org/10.1515/taa-2019-0002","url":null,"abstract":"Abstract The main aim of this paper is localization of the chain recurrent set in shape theoretical framework. Namely, using the intrinsic approach to shape from [1] we present a result which claims that under certain conditions the chain recurrent set preserves local shape properties. We proved this result in [2] using the notion of a proper covering. Here we give a new proof using the Lebesque number for a covering and verify this result by investigating the symbolical image of a couple of systems of differential equations following [3].","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"7 1","pages":"13 - 28"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2019-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48588746","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: 1
Topological entropy for locally linearly compact vector spaces and field extensions 局部线性紧向量空间和域扩展的拓扑熵
Topological Algebra and its Applications Pub Date : 2018-09-06 DOI: 10.1515/taa-2020-0005
I. Castellano
{"title":"Topological entropy for locally linearly compact vector spaces and field extensions","authors":"I. Castellano","doi":"10.1515/taa-2020-0005","DOIUrl":"https://doi.org/10.1515/taa-2020-0005","url":null,"abstract":"Abstract Let 𝕂 be a discrete field and (V, ϕ) a pair consisting of a locally linearly compact 𝕂-space V and a continuous endomorphism ϕ: V → V. We provide the formulae to compute the topological entropy ent* of the flow (V, ϕ) subject to either extension or restriction of scalars.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"8 1","pages":"58 - 66"},"PeriodicalIF":0.0,"publicationDate":"2018-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2020-0005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41339843","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: 5
Differential conditions for which near-rings are commutative rings 近环为交换环的微分条件
Topological Algebra and its Applications Pub Date : 2018-08-06 DOI: 10.1515/9783110542400-005
B. Abdelkarim, C. Abdelhakim, Zeriouh Mostafa
{"title":"Differential conditions for which near-rings are commutative rings","authors":"B. Abdelkarim, C. Abdelhakim, Zeriouh Mostafa","doi":"10.1515/9783110542400-005","DOIUrl":"https://doi.org/10.1515/9783110542400-005","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80369882","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
Generalized derivations on prime rings with involution 有对合的素环上的广义导数
Topological Algebra and its Applications Pub Date : 2018-08-06 DOI: 10.1515/9783110542400-024
O. A. Zemzami, A. Mamouni, L. Oukhtite
{"title":"Generalized derivations on prime rings with involution","authors":"O. A. Zemzami, A. Mamouni, L. Oukhtite","doi":"10.1515/9783110542400-024","DOIUrl":"https://doi.org/10.1515/9783110542400-024","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76558071","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: 4
Modules witnessing that a leavitt path algebra is directly infinite 证明莱维特路径代数是直接无穷的模块
Topological Algebra and its Applications Pub Date : 2018-08-06 DOI: 10.1515/9783110542400-015
S. López-Permouth, N. Pilewski
{"title":"Modules witnessing that a leavitt path algebra is directly infinite","authors":"S. López-Permouth, N. Pilewski","doi":"10.1515/9783110542400-015","DOIUrl":"https://doi.org/10.1515/9783110542400-015","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74754198","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: 3
Proper categories and their duals 适当的范畴及其对偶
Topological Algebra and its Applications Pub Date : 2018-08-06 DOI: 10.1515/9783110542400-018
P. G. Romeo, Sreejamol Panthallor Rajan
{"title":"Proper categories and their duals","authors":"P. G. Romeo, Sreejamol Panthallor Rajan","doi":"10.1515/9783110542400-018","DOIUrl":"https://doi.org/10.1515/9783110542400-018","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73212309","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 nakayama conjecture and related conjectures-review 中山猜想及相关猜想述评
Topological Algebra and its Applications Pub Date : 2018-08-06 DOI: 10.1515/9783110542400-019
Masahisa Sato
{"title":"On nakayama conjecture and related conjectures-review","authors":"Masahisa Sato","doi":"10.1515/9783110542400-019","DOIUrl":"https://doi.org/10.1515/9783110542400-019","url":null,"abstract":"","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73152085","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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