Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The existence of flat covers over Noetherian rings of finite Krull dimension
HTML articles powered by AMS MathViewer

by Jin Zhong Xu PDF
Proc. Amer. Math. Soc. 123 (1995), 27-32 Request permission

Abstract:

Bass characterized the rings R with the property that every left R-module has a projective cover. These are the left perfect rings. A ring is left perfect if and only if the class of projective R-modules coincides with the class of flat R-modules, so the projective covers over these rings are flat covers. This prompts the conjecture that over any ring R, every left R-module has a flat cover. Known classes of rings for which the conjecture holds include Von Neumann regular rings (trivially), the left perfect rings (Bass), Prufer domains (Enochs), and then more generally, all right coherent rings of finite weak global dimension (Belshoff, Enochs, Xu). In this paper we show that the conjecture holds for all commutative Noetherian rings of finite Krull dimension and so for all local rings and all coordinate rings of affine algebraic varieties.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16D40, 13C11
  • Retrieve articles in all journals with MSC: 16D40, 13C11
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 27-32
  • MSC: Primary 16D40; Secondary 13C11
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1242111-5
  • MathSciNet review: 1242111