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Dirichlet's theorem on primes in arithmetic progression: if $a$ and $b$ are any relatively prime positive integers, then there are infinitely many prime numbers of the form $a+nb$ for positive integer …

One can argue that commutative algebra is affine algebraic geometry. However, a great deal of commutative algebra generalizes to non-commutative algebra, and in that setting there is little geometry, …

A semiprime operation on a ring $R$ (commutative with identity) is a closure operation $c: I \longmapsto I^c$ on the lattice of all ideals of $R$ such that $I^c J^c \subseteq (IJ)^c$ for all ideals $I …

Question 1: The fraction field is the same as that of $\mathbb{Z}[[x]]$. It can be gotten by inverting all irreducibles. The irreducibles of the UFD $\mathbb{Z}[[x]]$ are described in Theorem 1.4 of …

Let $\eta$ be a closed convex subset of ${\mathbb R}^n$ of convex dimension $n$ (not necessarily compact) with nonempty boundary $\partial \eta$. Then $\eta$ is an $n$-dimensional topological manifol …