The local rings of global dimension two

Vasconcelos, Wolmer V.

doi:10.1090/S0002-9939-1972-0308115-6

The local rings of global dimension two
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by Wolmer V. Vasconcelos PDF

Proc. Amer. Math. Soc. 35 (1972), 381-386 Request permission

Abstract:

A commutative local ring A of global dimension two conforms to the following description: (a) If the maximal ideal M is either principal or not finitely generated then A is a valuation domain. (b) Otherwise M is generated by a regular sequence of two elements but the ring is not necessarily noetherian. It will be noetherian if and only if it is completely integrally closed.

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