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Global Krull Dimension and Global Dual Krull Dimension of Valuation Rings 评价环的全局Krull维数和全局对偶Krull维数
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-5
T. Albu, P. Vámos
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引用次数: 13
Building Noetherian Domains Inside an Ideal-adic Completion 在理想补全中构建诺瑟域
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-23
W. Heinzer, C. Rotthaus, S. Wiegand
{"title":"Building Noetherian Domains Inside an Ideal-adic Completion","authors":"W. Heinzer, C. Rotthaus, S. Wiegand","doi":"10.1201/9780429187605-23","DOIUrl":"https://doi.org/10.1201/9780429187605-23","url":null,"abstract":"Suppose a is a nonzero nonunit of a Noetherian integral domain R. An interesting construction introduced by Ray Heitmann addresses the question of how ring-theoretically to adjoin a transcendental power series in a to the ring R. We apply this construction, and its natural generalization to finitely many elements, to exhibit Noetherian extension domains of R inside the (a)-adic completion R∗ of R. Suppose τ1, . . . , τs ∈ aR∗ are algebraically independent over K, the field of fractions of R. Starting with U0 := R[τ1, . . . , τs], there is a natural sequence of nested polynomial rings Un between R and A := K(τ1, . . . , τs) ∩ R∗. It is not hard to show that if U := ∪n=0Un is Noetherian, then A is a localization of U and R∗[1/a] is flat over U0. We prove, conversely, that if R∗[1/a] is flat over U0, then U is Noetherian and A := K(τ1, . . . , τs) ∩ R∗ is a localization of U . Thus the flatness of R∗[1/a] over U0 implies the intersection domain A is Noetherian.","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126168212","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
K0 of Semiartinian Unit-Regular Rings 半分子单位-正则环的K0
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-8
G. Baccella, A. Ciampella
{"title":"K0 of Semiartinian Unit-Regular Rings","authors":"G. Baccella, A. Ciampella","doi":"10.1201/9780429187605-8","DOIUrl":"https://doi.org/10.1201/9780429187605-8","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127575063","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
Torsionless Modules and Rings with Finite Essential Socle 具有有限基本环的无扭模和环
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-22
J. G. Pardo, P. A. G. Asensio
{"title":"Torsionless Modules and Rings with Finite Essential Socle","authors":"J. G. Pardo, P. A. G. Asensio","doi":"10.1201/9780429187605-22","DOIUrl":"https://doi.org/10.1201/9780429187605-22","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133218852","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
AB-5* for Module and Ring Extensions AB-5*用于模块和环扩展
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-7
P. N. Ánh, Dolors Herbera, C. Menini
{"title":"AB-5* for Module and Ring Extensions","authors":"P. N. Ánh, Dolors Herbera, C. Menini","doi":"10.1201/9780429187605-7","DOIUrl":"https://doi.org/10.1201/9780429187605-7","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121357241","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 Thin Generating Sets in Topological Groups 论拓扑群中的瘦生成集
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-28
O. Okunev, M. Tkačenko
{"title":"On Thin Generating Sets in Topological Groups","authors":"O. Okunev, M. Tkačenko","doi":"10.1201/9780429187605-28","DOIUrl":"https://doi.org/10.1201/9780429187605-28","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130704548","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
The Variety of Topological Groups Generated by the Class of All Banach Spaces 全Banach空间类生成的拓扑群的变化
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-27
S. Morris, Carolyn E. McPhail
{"title":"The Variety of Topological Groups Generated by the Class of All Banach Spaces","authors":"S. Morris, Carolyn E. McPhail","doi":"10.1201/9780429187605-27","DOIUrl":"https://doi.org/10.1201/9780429187605-27","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131594343","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
Extensions of Compact Abelian Groups by Discrete Ones and Their Duality Theory, II 紧阿贝尔群的离散扩展及其对偶理论，2
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-18
L. Fuchs, K. Hofmann
{"title":"Extensions of Compact Abelian Groups by Discrete Ones and Their Duality Theory, II","authors":"L. Fuchs, K. Hofmann","doi":"10.1201/9780429187605-18","DOIUrl":"https://doi.org/10.1201/9780429187605-18","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121532128","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
The Lüroth’s Theorem for Some Complete Valued Fields 某些完全值域的l<s:1>罗斯定理
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-6
V. Alexandru, N. Popescu
{"title":"The Lüroth’s Theorem for Some Complete Valued Fields","authors":"V. Alexandru, N. Popescu","doi":"10.1201/9780429187605-6","DOIUrl":"https://doi.org/10.1201/9780429187605-6","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115376781","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
Orsatti’s Contribution to Topological Algebra Orsatti对拓扑代数的贡献
abelian groups, module theory, and topology Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-3
D. Dikranjan
{"title":"Orsatti’s Contribution to Topological Algebra","authors":"D. Dikranjan","doi":"10.1201/9780429187605-3","DOIUrl":"https://doi.org/10.1201/9780429187605-3","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126759050","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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