Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T13:17:38.559Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Representation of Modules by Sheaves of Factor Modules

Published online by Cambridge University Press:  20 November 2018

J. Lambek
J. Lambek*
Affiliation:
McGill University, Montreal, Quebec
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.

Throughout this paper we consider associative rings with unity elements. In §1 various results on the representation of rings by rings of sections of special rings are compared. In particular, it is shown that results enunciated by Dauns and Hofmann, Koh, and the present author may all be deduced from one statement, the proof of which appears in §3.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 359 - 368
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Birkhoff, G., Subdirect unions in universal algebra, Bull. Amer. Math. Soc. 31 (1935), 433-454.Google Scholar
2. Dauns, J. and Hofmann, K. H., The representation of a biregular ring by sheaves, Math. Z. 91 (1966), 103-123.Google Scholar
3. Dauns, J., Representation of rings by sections, Memoirs Amer. Math. Soc. 83, 1968.Google Scholar
4. Grothendieck, A. and Dieudonné, J., Eléments de géométrie algébrique I, I.H.E.S. Publications math. 4 Paris, 1960.Google Scholar
5. Koh, K., On functional representations of a ring without nilpotent elements, Canad. Math. Bull., (3) 14 (1971), 349-352.Google Scholar
6. Lambek, J., Lectures on rings and modules, Blaisdell, Waltham, 1966.Google Scholar
7. Lambek, J., Torsion theories, additive semantics, and rings of quotients, Springer Lecture Notes in Mathematics 177, 1971.Google Scholar
8. Lambek, J., Bicommutators of nice injectives, J. Algebra (to appear).Google Scholar
9. McCoy, N. H., Prime ideals in general rings, Amer. J. Math. 71 (1949), 823-833.Google Scholar
10. Pierce, R. S., Modules over commutative regular rings, Memoirs Amer. Math. Soc. 70 (1967).Google Scholar