Geodesic
Right Invariant Right Hereditary Rings
Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1186-1191

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Let R be a right hereditary domain in which all right ideals are two-sided (i.e., R is right invariant). We show that R is the intersection of generalized discrete valuation rings and that every right ideal is the product of prime ideals. This class of rings seems comparable with (and contains) the class of commutative Dedekind domains, but the rings considered here are in general not maximal orders and not Dedekind rings in the terminology of Robson [9]. The left order of a right ideal of such a ring is a ring of the same kind and the class contains right principal ideal domains in which the maximal right ideals are two-sided [6]. 
Brungs, H. H. Right Invariant Right Hereditary Rings. Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1186-1191. doi: 10.4153/CJM-1974-111-3
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