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ring of characteristic zero (remarkably easy for a q5)

Source: IMC 2000 day 1 problem 5

October 29, 2005
superior algebrasuperior algebra solvedRing Theory

Problem Statement

Let RR be a ring of characteristic zero. Let e,f,gāˆˆRe,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.
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