Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-04T21:14:13.330Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results on coherent rings II

Published online by Cambridge University Press:  18 May 2009

Morton E. Harris
Morton E. Harris
Affiliation:
The University of Illinoisat Chicago Circle
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

According to Bourbaki [1, pp. 62–63, Exercise 11], a left (resp. right) A-module M is said to be pseudo-coherent if every finitely generated submodule of M is finitely presented, and is said to be coherent if it is both pseudo-coherent and finitely generated. This Bourbaki reference contains various results on pseudo-coherent and coherent modules. Then, in [1, p. 63, Exercise 12], a ring which as a left (resp. right) module over itself is coherent is said to be a left (resp. right) coherent ring, and various results on and examples of coherent rings are presented. The result stated in [1, p. 63, Exercise 12a] is a basic theorem of [2] and first appeared there. A variety of results on and examples of coherent rings and modules are presented in [3].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 8 , Issue 2 , July 1967 , pp. 123 - 126
Copyright
Copyright © Glasgow Mathematical Journal Trust 1967

References

1.Bourbaki, N., Algèbre commutative, Chapitres 1–2, Hermann (Paris, 1961).Google Scholar
2.Chase, S. U., Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457–473.CrossRefGoogle Scholar
3.Harris, M. E., Some results on coherent rings, Proc. Amer. Math. Soc. 17 (1966), 474–479.CrossRefGoogle Scholar
4.Nagata, M., Some remarks on prime divisors, Mem. Coll. Sci. Univ. Kyoto Ser. A 33 (1960), 297–299.Google Scholar