Ideal is defined by:

if R is a Ring and I is subring of R, then

if r in I, and x in R then

r*x in I and x*r both in I

example of Ideal:

let R = Z, I = 2Z

r in Z

x in 2Z

then r*x = z*2Z = 2*Z

x*r = 2Z*Z = 2*Z

hence  2Z is an Ideal

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