A has property P iff A is a field
Source: Romanian MO 2010 Grade 12
August 6, 2012
algebrapolynomialRing Theorysuperior algebrasuperior algebra unsolved
Problem Statement
We say that a ring has property if any non-zero element can be written uniquely as the sum of an invertible element and a non-invertible element.
a) If in , , prove that has property if and only if is a field.
b) Give an example of a ring that is not a field, containing at least two elements, and having property .Dan Schwarz