Geodesic
On the Ring of Quotients at a Prime Ideal of a Right Noetherian Ring
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 703-712

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

J. Lambek and G. Michler [3] have initiated the study of a ring of quotients RP associated with a two-sided prime ideal P in a right noetherian ring R. The ring RP is the quotient ring (in the sense of [1]) associated with the hereditary torsion class τ consisting of all right R-modules M for which HomR(M, ER (R/P)) = 0, where ER (X) is the injective hull of the R-module X.In the present paper, we shall study further the properties of the ring RP. The main results are Theorems 4.3 and 4.6. Theorem 4.3 gives necessary and sufficient conditions for the torsion class associated with P to have property (T), as well as some properties of RP when these conditions are indeed satisfied, while Theorem 4.6 gives necessary and sufficient conditions for R to satisfy the right Ore condition with respect to (P). 
Heinicke, A. G. On the Ring of Quotients at a Prime Ideal of a Right Noetherian Ring. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 703-712. doi: 10.4153/CJM-1972-066-2
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[1] 1. Goldman, O., Rings and modules of quotients, J. Algebra 13 (1969), 10–47. Google Scholar

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[3] 3. Lambek, J. and Michler, G., The torsion theory at a prime ideal of a right noetherian ring (to appear). Google Scholar

[4] 4. Robson, J. C., Idealizers and hereditary noetherian prime rings (to appear). Google Scholar

[5] 5. Silver, L., Noncommutative localization and applications, J. Algebra 7 (1967), 44–76. Google Scholar

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