Geodesic
The Equality (A ∩ B)n = A n ∩ B n for Ideals
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 792-798

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Let D be an integral domain with identity, and let R be a commutative ring. If n is a positive integer, R will be said to have property (n), (n)′, or (n)′′ according asproperty (n): For any x, y ∊ R, (x, y)n = (xn, yn).property (n)′ : For any x ∊ R and any ideal A of R such that xn ∊ An, it follows that x ∊ A.property (n)′ : For any ideals A, B of R, (A ∩ B)n = An ∩ Bn.J. Ohm introduced property (n) in [7] in connection with the question: If n ≦ 2 and if D has property (n), must D be a Prüfer domain? (The integral domain D with identity is a Prüfer domain if each nonzero finitely generated ideal of D is invertible; equivalently, DP is a valuation ring for each proper prime ideal P of D.) Prior to Ohm's paper, it was known that if D has property (2) and if D is integrally closed, then D is Prüfer. 
Gilmer, Robert; Grams, Anne. The Equality (A ∩ B)n = A n ∩ B n for Ideals. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 792-798. doi: 10.4153/CJM-1972-076-9
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