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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

3 votes
1 answer
207 views

Weak approximation in Krull domains

Suppose $R$ is a Krull domain with the field of fraction $K$. To every prime ideal $P$ of $R$ of height $1$, one can associate a $ \mathbb{Z}$-valued discrete valuation which we denote by $v_P$. Suppo …
Keivan Karai's user avatar
  • 6,214
3 votes
0 answers
606 views

nilpotent matrices over polynomial rings

I am looking for an analogue of the Jordan normal form for nilpotent matrices over the polynomial ring ${\mathbb Z}[x_1, \dots, x_n]$. More precisely, is there a description for the orbits of action …
Keivan Karai's user avatar
  • 6,214
7 votes
2 answers
599 views

Zermelo's proof for unique factorisation

In Peter Bundschuh's "Einführung in die Zahlentheorie" I came across a possibly well-known but to me rather peculiar proof of unique factorisation, which is attributed to Ernst Zermelo. The proof bypa …
Keivan Karai's user avatar
  • 6,214
5 votes
1 answer
219 views

Intrinsic characterisation of a class of rings

This may be well known, but I was unable to find an answer browsing literature. Let us temporarily call a commutative (unital) ring $R$ an O-ring if there exists an integer $n \ge 1$, a local field of …
Keivan Karai's user avatar
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