An ideal $\mathfrak{a}$ is called irreducible if $\mathfrak{a} = \mathfrak{b} \cap \mathfrak{c}$ implies $\mathfrak{a} = \mathfrak{b}$ or $\mathfrak{a} = \mathfrak{c}$. Atiyah-Mac …

Let A be a commutative ring with 1 not equal to 0. (The ring A is not necessarily a domain, and is not necessarily noetherian.) Assume we have an injective map of free A-modules …

Be done the triangle ABC, it is known the method to finding the point Q that minimises the sum QA+QB+QC among all points Q in the plane (The Fermat point). I want a hint for solvin …

I'm reading Madsen and Tornehave's "From Calculus to Cohomology" and tried to solve this interesting problem regarding knots. Let $\Sigma\subset \mathbb{R}^n$ be homeomorphic to …

Three problems from G.Rosenstein "Linear orderings" (from the end of Chapter 2 and beginning of Chapter 4): 1) Is there a nondecreasing function from irrationals onto reals? 2) I …

I found the following exercise in Vistoli's notes. He proves a theorem stating that any category $\mathcal{F}$ fibered over $\mathcal{C}$ is equivalent, as a fibered category, to a …