Geodesic
Remarks on Op and Towber Rings
Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1109-1117

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

In this paper all rings considered have identity and are commutative, and all modules are finitely generated. We shall make liberal use of the definitions and notation established in [6; 7].Towber observed in [9] that a local Outer Product ring (OP-ring) must have v-dimension ≦ 2, and so a local OP-ring is either regular of global dimension ≦ 2 or it has infinite global dimension. Since the global dimension of a noetherian ring is the supremum of the global dimensions of its localizations, we immediately obtain the following result.THEOREM 1.1. The global dimension of a noetherian OP-ring is either∞ or ≦ 2. 
Lissner, David; Geramita, Anthony. Remarks on Op and Towber Rings. Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1109-1117. doi: 10.4153/CJM-1970-128-6
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