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# Questions tagged [topological-rings]

This is intended to include topological fields as well.

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### Topology of the Malcev-Neumann group ring

For a ring $R$ and a group $G$ the group ring $R[G]$ consist of maps from $G$ to $R$ with finite support. It was shown that if the group is fully ordered them this ring can be embedded in a division ... 43 views

### Topological rings with a final topology

Given a family of ring homomorphisms $\phi_i : X \rightarrow Y_i$ where each $Y_i$ is a topological ring and consider the initial topology on $X$, i.e. the coarest topology such that each map is ... 127 views

### Ideals of an ordered ring

Suppose $R$ is a strictly ordered (non-commutative) ring, in particular $ab > 0$ for any $a,\, b > 0$, that is also discrete in that there are no elements between $0$ and $1$. Now consider a two-... 130 views

### Embedding a monoid into a group via its monoid ring

Suppose I have a monoid $(M,\, \cdot,\, e)$ equipped with a monoid homomorphism $\textrm{length} : M \rightarrow \mathbb{N}_+$ into the monoid of natural numbers under addition where $e$ is the only ... 285 views

### What is the status of topological problems in group rings?

I have extensively studied group rings and structure of their units and also zero divisors and normalizer problem in integral group rings.. I was pondering upon questions like what if we use ...
114 views

### Initial topology for a topological ring

Given a topological ring $R$ and an arbitrary (thus not necessarily surjective) epimorphism $q: R \to S$ of underlying rings is there a finest topology on $S$ such that 1) $S$ is a topological ring ...
222 views

### Regular epimorphisms in the category of topological rings

I am cross-posting this question from math stack exchange (link below) as it has not received any comments or answers over the past month. A regular epimorphism is a morphism $f: X \to Y$ that is the ...
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1 vote
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### Properties of differentiable functions on non-locally-bounded fields

I was reading some results on the structure of non-locally-bounded topological fields, and I was wondering what is known about differentiable functions on them. In particular, on the complex numbers ...
396 views

### Krull dimension of completions in non-noetherian setting (especially completed perfections)

What are some general results describing the Krull dimension of the completion of a non-Noetherian ring with a "nice" topology? An example of the sort of "nice" topological ring I'm looking for is a ...
1 vote
I am trying to understand the completed tensorproduct. This can be defined as follows: Given a topological ring $R$ and two linearly topologized rings $A$ and $B$ with fundamental systems of open ...