Apr 21, 2020 · Gauss’s own statement of the Lemma is in his Disquisitiones Arithmeticae, and to be honest, is closer to your statement than mine. In fact, it is the contrapositive of the “if” clause of your …

Proof of Gauss's Lemma (Riemannian Geometry version) Ask Question Asked 13 years, 5 months ago Modified 13 years, 5 months ago

Aug 16, 2018 · 2 I would direct you to my Monthly paper with David McKinnon for a general discussion on Gauss's Lemma and unique factorization. The key is to use unique factorization in $\mathbb {Q} …

Dec 15, 2022 · @ducksforever See the extensive survey by D.D. Anderson cited here for generalizations of Gauss's Lemma and related results.

Apr 9, 2017 · 5 Gauss's Lemma for polynomials claims that a non-constant polynomial in $\mathbb {Z} [X]$ is irreducible in $\mathbb {Z} [X]$ if and only if it is both irreducible in $\mathbb {Q} [X]$ and …

Gauss Lemma for quadratic residues Ask Question Asked 12 years, 3 months ago Modified 1 year, 7 months ago

4 Do Carmo's formulation is ambiguous, and he does not mean that the Gauss Lemma implies that the boundary of a geodesic ball is an hypersurface. The author might have prefered this formulation: The …

Nov 1, 2023 · This is sometimes called the Gauss-Kronecker Lemma, or Dedekind's Prague Theorem. Dedekind discovered a form applying to algebraic integers after studying a divisor-theoretic form that …

Nov 19, 2024 · I am trying to understand the proof of this corollary to Gauss's lemma found in Abstract Algebra (Theory and Applications) by Thomas W. Judson. Here is the link to a screenshot of the …

Jan 24, 2023 · Gauss's Lemma: Let f, g ∈ R[x] f, g ∈ R [x] be primitive. Then fg f g is also primitive. The proof proceeds by the following. We want to show that for an arbitrary irreducible element p p of R R, …