{"title":"Normality in Hopf-Galois extensions","authors":"T. Crespo, A. Rio, M. Vela","doi":"10.1090/surv/260/08","DOIUrl":"https://doi.org/10.1090/surv/260/08","url":null,"abstract":"","PeriodicalId":311524,"journal":{"name":"Mathematical Surveys and Monographs","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130758515","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":"Persistence Theory - From Quiver Representations to Data Analysis","authors":"S. Oudot","doi":"10.1090/surv/209","DOIUrl":"https://doi.org/10.1090/surv/209","url":null,"abstract":"* Theoretical foundations: Algebraic persistence* Topological persistence* Stability Applications: Topological inference* Topological inference 2.0* Clustering Signatures for metric spaces* Perspectives: New trends in topological data analysis* Further prospects on the theory* Introduction to quiver theory with a view toward persistence* Bibliography* List of figures* Index","PeriodicalId":311524,"journal":{"name":"Mathematical Surveys and Monographs","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124079039","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":"Multi-ideal-adic completions of Noetherian rings","authors":"W. Heinzer, C. Rotthaus, S. Wiegand","doi":"10.1307/MMJ/1220879416","DOIUrl":"https://doi.org/10.1307/MMJ/1220879416","url":null,"abstract":"Let R be a commutative ring with identity. A filtration on R is a decreasing sequence {In}∞n=0 of ideals of R. Associated to a filtration is a well-defined completion R∗ = lim ←− R/In and a canonical homomorphism ψ : R → R ∗ [13, Chap. 9]. If ⋂∞ n=0 In = (0), then ψ is injective and R may be regarded as a subring of R∗ [13, p. 401]. In the terminology of Northcott, a filtration {In}∞n=0 is multiplicative if I0 = R and InIm ⊆ In+m for all m ≥ 0 and n ≥ 0 [13, p. 408]. A well-known example of a multiplicative filtration on R is the I -adic filtration {I n}∞n=0, where I is a fixed ideal of R. In this paper we consider filtrations of ideals of R that are not multiplicative and examine the completions associated to these filtrations. We assume the ring R is Noetherian. Instead of successive powers of a fixed ideal I, we use a filtration formed from a more general descending sequence {In}∞n=0 of ideals. We require, for each n > 0, that the nth ideal In be contained in the nth power of the Jacobson radical of R and that Ink ⊆ I k n for all k, n ≥ 0. We call the associated completion a multi-adic completion and denote it by R∗. The basics of the multi-adic construction and the relationship between this completion and certain ideal-adic completions are considered in Section 2. In Section 3 we prove, for {In} as just described, that R∗ is Noetherian. Let (R, m) be a Noetherian local ring. If R is excellent, Henselian, or universally catenary, we prove in Section 4 that R∗ has the same property. We were inspired to pursue this project partly because of our continuing interest in exploring completions and power series. In our previous work we constructed various examples of rings inside relatively well-understood rings such as the (x)adic completion k[y][[x]] of a polynomial ring k[x, y] in two variables x and y over a field k [4; 5]. The examples we obtained demonstrate that certain properties of a ring may fail to extend to its m-adic completion, where m is a maximal ideal [6]. The process of passing to completion gives an analytic flavor to algebra. Often we view completions in terms of power series or in terms of coherent sequences, as","PeriodicalId":311524,"journal":{"name":"Mathematical Surveys and Monographs","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130429209","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":"Integral Domains Inside Noetherian Power Series Rings","authors":"W. Heinzer, C. Rotthaus, S. Wiegand","doi":"10.1090/surv/259","DOIUrl":"https://doi.org/10.1090/surv/259","url":null,"abstract":"","PeriodicalId":311524,"journal":{"name":"Mathematical Surveys and Monographs","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127371773","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":"Stable and semistable Hopf-Galois extensions","authors":"","doi":"10.1090/surv/260/14","DOIUrl":"https://doi.org/10.1090/surv/260/14","url":null,"abstract":"","PeriodicalId":311524,"journal":{"name":"Mathematical Surveys and Monographs","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127936493","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":"Triple arrows for FA","authors":"","doi":"10.1090/surv/264/05","DOIUrl":"https://doi.org/10.1090/surv/264/05","url":null,"abstract":"","PeriodicalId":311524,"journal":{"name":"Mathematical Surveys and Monographs","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130438447","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
求助内容：
应助结果提醒方式：