Geodesic
On a Class of Archimedean Integral Domains
Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 365-375

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

Our starting point is an observation in elementary number theory [10, Exercise 26, p. 17]: if a and b are positive integers such that each number in the sequence a, b2, a3, b4, ... divides the next, then a = b. Its proof depends only on Z being a unique factorization domain (UFD) whose units are 1, —1. Accordingly, we abstract and say that a (commutative integral) domain R satisfies (*) in case, whenever nonzero elements a and b in R are such that each element in the sequence a, b2, a3, b4, ... divides the next, then a and b are associates in R (that is, a = bu for some unit u of R). The main objective of this paper is the study of the class of domains satisfying (*). 
Beauregard, Raymond A.; Dobbs, David E. On a Class of Archimedean Integral Domains. Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 365-375. doi: 10.4153/CJM-1976-038-x
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