MathOverflow

In the paper, "A universal characterization of higher algebraic K-theory", available for example as arXiv:1001.2282, Blumberg, Gepner, and Tabuada give a characterization of the Dennis trace map $K \rightarrow HH$ as the unit $1 \in \pi_0 \operatorname...

Let $k$ be a field and $h := x^2 + y^2 - 1 \in k[x,y]$.
Consider the following purely algebraic statement (★):
There do not exist $P,Q \in k[x,y]$, generating the unit ideal in $k[x,y]$, such that $P \equiv x \pmod{h}$ and $Q \equiv y \pmod{h}$.

Let $A$ be a zero-dimensional ring. I am interested in examples showing how the topology of the ring (in this very simple case where the dimension is zero) may influence properties of modules. In particular, I am curious whether certain classes of modules...

Before diving deep into the work itself, i want to make a short introduction to the history of the manuscript ( history of why this manuscript is not accepted by academic journals ) which is the main thing that we will talk about.
I am an Electronics Communication Engineer, my main motive for such work wasnt for academic sense. I was planning to make calibration and testing depending on this "mathematical" (if you would call it) work. So dont assume that this work is solely done...