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## Homework Statement

Determine the nilpotent, idempotents and units in

a) F[x]/<x

^{2}-x>

b) F[x]/<x

^{2}>

## Homework Equations

## The Attempt at a Solution

How do I do this without a specified Field?

For a) the elements in R would be {a+bx: a,b are in F; x

^{2}=x}

b) {a+bx: a,b in F; x

^{2}=0}

I know what it means to be idempotent, nilpotent and a unit, I just don't understand how I can pin point exact elements without knowing the field.