Geodesic
Rings with Enough Invertible Ideals
Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 131-144

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

All rings are associative with identity element 1 and all modules are unital. A ring has enough invertible ideals if every ideal containing a regular element contains an invertible ideal. Lenagan [8, Theorem 3.3] has shown that right bounded hereditary Noetherian prime rings have enough invertible ideals. The proof is quite ingenious and involves the theory of cycles developed by Eisenbud and Robson in [5] and a theorem which shows that any ring S such that R ⊆ S ⊆ Q satisfies the right restricted minimum condition, where Q is the classical quotient ring of R. In Section 1 we give an elementary proof of Lenagan's theorem based on another result of Eisenbud and Robson, namely every ideal of a hereditary Noetherian prime ring can be expressed as the product of an invertible ideal and an eventually idempotent ideal (see [5, Theorem 4.2]). We also take the opportunity to weaken the conditions on the ring R. 
Smith, P. F. Rings with Enough Invertible Ideals. Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 131-144. doi: 10.4153/CJM-1983-009-8
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