# Questions tagged [topological-rings]

This is intended to include topological fields as well.

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### Perturbing pole of Laurent polynomial/series in a single summand

I am working with the ring of Laurent polynomials $\mathbb{F}[X,X^{-1}]$ over $\mathbb{F}$ for some algebraically closed field $\mathbb{F}$ of any characteristic. I encountered a problem emerging from ...
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1 vote
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### Topological modules over a locally compact ring

Let $R$ be a locally compact, separably metrizable ring (commutative with an identity) and let $M$ be a closed submodule of $R \oplus R$. Is the projection of $M$ onto the first coordinate closed?
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### Are topological PID's Noetherian?

Romain Giquaud has given a counterexample to the general form of the question. The bounty is for a solution for locally compact, metrizable rings. (I suspect the answer may be positive with this ...
• 42.2k
84 views

### 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 ...
133 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-...
155 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 ...
296 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 ...
122 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 ...
• 103
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### 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 ...
• 111
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### 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 ...
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1 vote
119 views

### Completed Tensorproduct

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 ...
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