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Remarks on Op and Towber Rings

Published online by Cambridge University Press:  20 November 2018

David Lissner  and
Anthony Geramita
David Lissner
Affiliation:
Syracuse University, Syracuse, New York
Anthony Geramita
Affiliation:
Queen's University, Kingston, Ontario
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 6 , 01 December 1970 , pp. 1109 - 1117
Copyright
Copyright © Canadian Mathematical Society 1970

References

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