MathDB
Show that a certain ring of fractions is factorial

Source: SNSB Adission 2003

October 8, 2019
number theoryprime numbersRing Theoryfactorial

Problem Statement

Let be a prime number p, p, the quotient ring R=Z[X,Y]/(pX,pY), R=\mathbb{Z}[X,Y]/(pX,pY), and a prime ideal I⊃pA I\supset pA that is not maximal. Show that the ring {r/i∣r∈R,i∈I} \left\{ r/i|r\in R, i\in I \right\} is factorial.
Back to ProblemsView on AoPS