MathDB

5

Part of 2000 IMC

Problems(2)

ring of characteristic zero (remarkably easy for a q5)

Source: IMC 2000 day 1 problem 5

10/29/2005
Let RR be a ring of characteristic zero. Let e,f,g∈Re,f,g\in R be idempotent elements (an element xx is called idempotent if x2=xx^2=x) satisfying e+f+g=0e+f+g=0. Show that e=f=g=0e=f=g=0.
superior algebrasuperior algebra solvedRing Theory
functional equation

Source: IMC 2000 day 2 problem 5

10/29/2005
Find all functions R+→R+\mathbb{R}^+\rightarrow\mathbb{R}^+ for which we have for all x,y∈R+x,y\in \mathbb{R}^+ that f(x)f(yf(x))=f(x+y)f(x)f(yf(x))=f(x+y).
functionalgebradomainsymmetryreal analysisreal analysis unsolved