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Remarks on Op and Towber Rings
Published online by Cambridge University Press: 20 November 2018
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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.
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