Over a decade ago I uncovered a coverage problem with the ring of algebraic integers and had a paper published in a now dead math journal, which died a few years after publishing and withdrawing my paper, despite having existed over a decade prior.

Continuing the research path of the paper I have since been able to explain the coverage problem far more simply, using elementary methods:

somemath.blogspot.com/2012/11/some-weird-math.html

So what are its consequences?

For fields, it has none because the field of algebraic numbers as a ratio of algebraic integers does not have this problem, though I have shifted to thinking of it as a ratio of objects, from my object ring, which I discovered to fix the coverage issue.

For the ring of algebraic integers the coverage problem allows you to appear to prove two different and contradictory mathematical statements! Which is what my original paper covered.

James Harris