abelian groups, module theory, and topology最新文献

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On a Duality with “Less than Usual” Reflexive Abstract Modules 关于具有“不常”自反抽象模的对偶性

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-35

A. Tonolo

引用次数: 0

Subgroups of the Baer-Specker Group with Prescribed Endomorphism Ring and Large Dual 具有规定自同态环和大对偶的Baer-Specker群的子群

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-12

A. Corner, R. Göbel

引用次数: 1

G-Minimal Topological Groups g -极小拓扑群

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-24

M. Megrelishvili

We study suucient conditions for G-minimality of topological G-groups X and minimality of semidirect products X hG arising under some natural constructions .

研究了在某些自然构造下拓扑g群X的g极小性和半直积X hG的极小性的充分条件。

引用次数: 6

A Theorem on Extensions of Bimodules 关于双模扩展的一个定理

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-15

G. D'este

引用次数: 0

The Roelcke Compactification of Unitary Groups 酉群的Roelcke紧化

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-36

V. Uspenskij

引用次数: 2

Orsatti’s Contribution to Module Theory Orsatti对模块理论的贡献

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-2

C. Menini

I met Adalberto for the first time in November 1972: I was a first year student in Mathematics and he was my Algebra Professor. I do remember those tough days pretty well: the word “set” was completely new to me and each every time, at the end of Adalberto’s lesson, I thought I got an Arabic class instead of an Algebra one. Then suddenly, during Christmas time, I felt I could understand everything and that everything was so beautiful that, in the end, I gave up a very fancy interest for cybernetics (!) and decided to get more Algebra courses. Thus, in the next years, I followed two more courses by Adalberto and also got the honour to have him as my thesis advisor. Since then a never-ended collaboration began. Adalberto is not only a very clear teacher; he has the special gift of capturing your attention leading you inside the subject. For me he is the most fascinating person I ever met during my mathematical experience. And not only this. He taught me the most difficult thing: how to do research. It is nice here to remember that each every time I was getting depressed because we were not able to prove something then he began telling me one of his incredible jokes. Also if we found out that something we would have liked to be true, it was not, he was telling me “This is the truth, Claudia, what do you want more then the truth?” Orsatti’s first work in module theory is his first paper on Duality [O1]. The astonishing idea he got was that Pontryagin duality between discrete and compact abelian groups (see [P1] and [P2]) and Lefschetz duality (see [L]) between discrete and linearly compact vector spaces as well as Kaplansky’s (see [K]) and Macdonald’s (see [Mc]) generalizations of this last one could be all thought as a particular case of a much more general situation. Namely, let A be a commutative ring and K an Hausdorff complete topological module over the ring A endowed with its discrete topology. Assume that: P1) The mapping a 7→ μa= multiplication by a in K defines an isomorphism A ∼= ChomA(K, K). P2) K has no small submodules i.e. there is a neighbourhood U of 0 in K such that the only submodule of K contained in U is 0. Let A-TM denote the category of Hausdorff topological modules over the ring A endowed with its discrete topology and let C(KA) be the subcategory of A-TM consisting of those topological modules which are topological isomorphic to closed submodules of topological products of copies of K. Let D(KA) be the subcategory of Mod-A cogenerated by KA. For every M ∈ Mod-A let M∗ be the A-module HomA(M,K) endowed with the topology of pointwise convergence. Clearly M∗ ∈ C(KA). For every M ∈ A-TM, let M∗ be the abstract module ChomA(M, K);

我第一次见到阿达伯托是在1972年11月，当时我是数学系的一年级学生，他是我的代数教授。我清楚地记得那些艰难的日子:“集合”这个词对我来说是完全陌生的，每次阿达伯托的课结束时，我都以为我上的是阿拉伯语课，而不是代数课。突然，在圣诞节期间，我觉得我可以理解一切，一切都是如此美好，以至于最后，我放弃了对控制论的浓厚兴趣，决定去学习更多的代数课程。因此，在接下来的几年里，我又学习了Adalberto的两门课程，并有幸得到了他作为我的论文指导老师。从那时起，一场永无止境的合作开始了。阿达伯托不仅是一位非常清晰的老师;他有一种特殊的天赋，能抓住你的注意力，引导你进入主题。对我来说，他是我数学生涯中遇到的最迷人的人。不仅如此。他教会了我最难的事情:如何做研究。每当我因为我们无法证明什么而感到沮丧时，他就开始给我讲他的一个不可思议的笑话。此外，如果我们发现我们希望是真的，但事实并非如此，他会告诉我:“这就是真相，克劳迪娅，除了真相，你还想要什么?”Orsatti在模论方面的第一部作品是他关于对偶的第一篇论文[01]。他得到的令人惊讶的想法是离散和紧致阿贝群之间的庞特里亚金对偶(见[P1]和[P2])和离散和线性紧致向量空间之间的Lefschetz对偶(见[L])，以及最后一个的推广，都可以被认为是一个更一般情况下的特殊情况。即设A是一个交换环，且环A上具有离散拓扑的Hausdorff完全拓扑模。假设:P1)映射a 7→μa=乘以a在K中定义了一个同构a ~ = ChomA(K, K)。P2) K没有小的子模，即在K中存在一个邻域U = 0，使得K在U中包含的唯一子模为0。设A- tm表示具有离散拓扑的环A上的Hausdorff拓扑模的范畴，设C(KA)是由与k的副本拓扑积的闭合子模拓扑同构的拓扑模组成的A- tm的子范畴，设D(KA)是KA余生的Mod-A的子范畴。对于每一个M∈Mod-A，设M *为具有点向收敛拓扑的a模HomA(M,K)。显然M∗∈C(KA)。对于每一个M∈A-TM，设M∗为抽象模ChomA(M, K);

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引用次数: 1

List of Adalberto Orsatti’s Publications Adalberto Orsatti的出版物列表

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-4

引用次数: 0

Commutative Rings with Acc on Irreducible Ideals 不可约理想上带Acc的交换环

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-16

C. Faith

引用次数: 0

On a Problem of Prof. A. Orsatti 论奥萨蒂教授的一个问题

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-11

G. Călugăreanu

引用次数: 0

Suitable Sets in Products of Topological Groups and in Groups Equipped with the Bohr Topology 拓扑群积和具有玻尔拓扑的群中的合适集

abelian groups, module theory, and topology

Pub Date : 2019-05-16 DOI: 10.1201/9780429187605-34

A. H. Tomita, F. Trigos-Arrieta

引用次数: 0

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