3 Let I be an ideal of the ring R and define the set ann (1) ={rERIra=o, VaE Prove that ann (I) forms ideals Cann (I)is alled annihd ate of I)

Theorem (3-6):- Let f:(R,+, .) → (R',+` , .) be a ring. homo , onto function and 1- If (R,+, .) is commutative ring with identity 1. Then (R`,+,.) is also commutative ring with identity 1. 2-If (R,+, .) is a ring without zero divisors, Then (R,+,.) is also a ring without zero divisors.

Let R be a commutative ring such that a^2 = a for all a ∈ R, then show that a+a = 0.

Let P be a prime ideal and R a commutative ring with identity. If R/P is an integral domain, explain why R/P cannot be the ring with one element. Also explain why P is not equal to R in this scenario.