Geodesic
A Shorter Proof of Goldie's Theorem
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 597-602

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

In this note we present an extremely short proof of Goldie's theorem on the structure of semiprime Noetherian rings [1]. The outline of the proof was given by Procesi and Small in [4]. By utilizing the concept of the singular ideal of a ring we have been able to weaken the hypotheses of many of the steps in [4]. Most significantly, we are able to avoid a reduction to the case of prime rings, and in Lemma 5 we give an informative list of the relationship between regular elements and essential ideals of semiprime rings. 
Zelmanowitz, Julius. A Shorter Proof of Goldie's Theorem. Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 597-602. doi: 10.4153/CMB-1969-077-1
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[1] 1. Goldie, A. W., Semiprime rings with maximum condition, Proc. Lond. Math. Soc. 10 (1960) 201–220. Google Scholar

[2] 2. Jacobson, Z. N., Structure of rings (revised edition). Vol. 37, A.M. S. Colloq. (Providence, 1964). Google Scholar

[3] 3. Johnson, R. E. and Wong, E. T., Self-injective rings. Canad. Math. Bull. 2 (1959) 167–173. Google Scholar

[4] 4. Procesi, C. and Small, L., On a theorem of Goldie. Jour. Algebre 2 (1965) 80–84. Google Scholar

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