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Exercise 12. Prove that every subring of a commutative ring is commutative. Exercise 13. Give an example of non-commutative ring contains a commutative su- bring

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Exercise 12. Prove that every subring of a commutative ring is commutative. Exercise 13. Give an example of non-commutative ring contains a commutative su- bring with proof. Exercise 14. Give an example of a ring with identity (R. +..) such that contains a subring without identity with proof. Exercise 15. Give an example of a ring without identity (R, +..) such that contains a subring has an identity with proof. Exercise 16. Give an example of a ring (R. +..) with identity IR and a subring (S,+..) with identity 1s such that IR+ls with proof. H.W The flow defined as v = Prove it is an incompressible flow and find its streamfunctions. 1-A man borrows $ 17,532 to buy a car at an annual interest rate of 3%. The loan will be paid in monthly installments in 4 years installments, with the first installment to be paid one month after the loan is released. What is the monthly installment he has to pay? T-A man wants to save $35,935 to pay for his son's education within 3 years. time an Education Fund requires investors to deposit equal installments annually at the end of each year. If interest of 3,37%was paid, how much would a man have to save each year to achieve his goal? help me please

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