Geodesic
Generalized Discrete Valuation Rings
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1404-1408

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

Jategaonkar (5) has constructed a class of rings which can be used to provide counterexamples to problems concerning unique factorization in non-commutative domains, the left-right symmetry of the global dimension for a right- Noetherian ring and the transhnite powers of the Jacobson radical of a right- Noetherian ring. These rings have the following property:(W) Every non-empty family of right ideals of the ring R contains exactly one maximal element.In the present paper we wish to consider rings, with unit element, which satisfy property (W). This property means that the right ideals are inverse well-ordered by inclusion, and it is our aim to describe these rings by their order type. Rings of this kind appear as a generalization of discrete valuation rings in R; see (1; 2).In the following, R will always denote a ring with unit element satisfying (W). 
Brungs, H.-H. Generalized Discrete Valuation Rings. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1404-1408. doi: 10.4153/CJM-1969-154-x
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