Geodesic
On a Condition of J. Ohm for Integral Domains1
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 970-983

Voir la notice de l'article provenant de la source Cambridge University Press

This paper originated mainly from results presented in a paper by J. Ohm (13), and, to a lesser degree, from results of Gilmer in (3). Ohm's paper is concerned with the validity of the equation (x, y)n = (xn, yn) for each pair of elements x, y of an integral domain D with identity. If D is a Prüfer domain, the above equation is valid for all x, y ε D (7, p. 244). Butts and Smith have shown (2) that if (x, y)2 = (x 2, y 2) for all x, y of the integrally closed domain D, then D is a Priifer domain. 
Gilmer, Robert. On a Condition of J. Ohm for Integral Domains1. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 970-983. doi: 10.4153/CJM-1968-095-2
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