This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 1

2002 District Olympiad, 2
Tags: superior algebra , product rings , ring theory , morphism
[b]a)[/b] Show that, for any distinct natural numbers $ m,n, $ the rings $ \mathbb{Z}_2\times \underbrace{\cdots}_{m\text{ times}} \times\mathbb{Z}_2,\mathbb{Z}_2\times \underbrace{\cdots}_{n\text{ times}} \times\mathbb{Z}_2 $ are homomorphic, but not isomorphic. [b]b)[/b] Show that there are infinitely many pairwise nonhomomorphic rings of same order.