@MartinSleziak Thanks for informing me about this discussion on meta. No doubt that factorization theory should not have a top-level tag. But concerning the use of "-theory", I beg to disagree: Please search for "Factorization" at commalg.org/surveys. For a relatively long time, this area of research has been viewed as a rather marginal subfield of commutative algebra, as it used to be almost entirely focuses on cancellative commutative monoids (the first source of examples being integral domains). But the situation has slightly changed in recent years. — Salvo Tringali 45 secs ago
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let $L=\mathbb{Q}(\sqrt[5]{n},\zeta_5)$ and $K=\mathbb{Q}(\zeta_5)$ the $5^{th}$ cyclotomic fields, we now that $[L:K] = 5$ and $ GAl(L/K) =\langle\sigma\rangle$ so we call $\mathcal{A}$ an ambigous ideal class of the extension $L/K$ if and only if $\mathcal{A}^{\sigma}= \mathcal{A}$.
My questi...
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Given a finite set of convex $d$-dimensional polytopes $\mathcal P$, for some $d\ge 2$.
Question: Is it true that there are only finitely many different convex $(d+1)$-dimensional polytopes whose facets are solely (scaled and rotated versions of) polytopes in $\mathcal P$?
Some clarificat...
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Ok, so I try to formulate rigorously the question in the title, for which I am asking for references. My definitions may be flawed, so feel free to adjust/correct them! I care about dimensions 2 and 3 below, but feel free to mention general d as well.
Let $d\ge 1$ be an integer, $G=(V,E)$ be a g...
