An ideal of a commutative ring R is said to be finitely generated if there exist elements a₁ , . . . , an in R such that every element r ∈ R can be written as a₁r₁ + · · · + aₙrₙ for some r1, . . . , rn in R. Prove that R satisfies the ascending chain condition if and only if every ideal of R is finitely generated.