Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1972-0308115-6
MathSciNet review: 0308115
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13H99

Retrieve articles in all journals with MSC: 13H99


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0308115-6
Keywords: Projective dimension, global dimension, coherent ring, prime ideal, flat module, finitistic dimension
Article copyright: © Copyright 1972 American Mathematical Society