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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The local rings of global dimension two

Author: Wolmer V. Vasconcelos
Journal: Proc. Amer. Math. Soc. 35 (1972), 381-386
MSC: Primary 13H99
MathSciNet review: 0308115
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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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Keywords: Projective dimension, global dimension, coherent ring, prime ideal, flat module, finitistic dimension
Article copyright: © Copyright 1972 American Mathematical Society

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