Geodesic
On Maximal Torsion Radicals, II
Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 115-120

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

Let R be an associative ring with identity, and let denote the category of unital left R-modules. The Walkers [6] raised the question of characterizing the maximal torsion radicals of , and showed that if R is commutative and Noetherian, then there is a one-to-one correspondence between maximal torsion radicals and minimal prime ideals of R [6, Theorem 1.29]. Popescu announced [5, Theorem 2.5] that the result remains valid for commutative rings with Gabriel dimension (in the terminology of [2]). Theorem 4.6 below shows that the result holds for rings (not necessarily commutative) with Krull dimension on either the left or right, extending the previous theorem for right Noetherian rings which appeared in [1]. 
Beachy, John A. On Maximal Torsion Radicals, II. Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 115-120. doi: 10.4153/CJM-1975-014-2
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[1] 1. Beachy, John A., On maximal torsion radicals, Can. J. Math. 25 (1973), 712–726. Google Scholar

[2] 2. Gordon, Robert and Robson, J. C., Krull dimension, Mem. Amer. Math. Soc. (to appear in No. 133, 1973). Google Scholar

[3] 3. Lambek, Joachim, Lectures on rings and modules (Blaisdell: Waltham, Toronto, London, 1966). Google Scholar

[4] 4. Lambek, Joachim, Torsion theories, additive semantics, and rings of quotients, Lecture Notes in Math 177 (Springer-Verlag, 1971). Google Scholar

[5] 5. Popescu, Nicolaie, Les anneaux semi-noetheriens, C. R. Acad. Sci. Paris Ser. A-B 272 (1971), 1439–1441. Google Scholar

[6] 6. Walker, Carol L. and Walker, Elbert A., Quotient categories and rings of quotients, Rocky Mountain J. Math. 2 (1972), 513–555. Google Scholar

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