Q: Is 2ℤ an ideal of ℤ? Is {0,2,4} a subring of ℤ₆? An ideal? 2ℤ: r(2k) = 2(rk) ∈ 2ℤ ✓: IDEAL (absorbs multiplication!)! {0,2,4} ≤ ℤ₆: subring ✓ (closed +,×!). Ideal? 3·2 = 6 = 0 ∈ set; 5·2 = 10 = 4 ∈: check all: IDEAL ✓! (Every subring of ℤₙ... not always ideal!)