MathDB
Z_2...Z_2,Z_2...Z_2 homomorphic;

Source: Romanian District Olympiad, Grade XII, Problem 2

October 7, 2018
superior algebramorphismsproduct ringsRing Theory

Problem Statement

a) Show that, for any distinct natural numbers m,n, m,n, the rings Z2×⋯⏟m times×Z2,Z2×⋯⏟n times×Z2 \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) Show that there are infinitely many pairwise nonhomomorphic rings of same order.
Back to ProblemsView on AoPS