Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-16T01:48:35.393Z Has data issue: false hasContentIssue false
  • English
  • Français

The Maximal Co-Rational Extension by a Module

Published online by Cambridge University Press:  20 November 2018

R. C. Courter
R. C. Courter*
Affiliation:
University of Windsor, Windsor, Ontario
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.

Modules are S-modules where S is an arbitrary ring with or without a unit element. We consider a projective module P having a submodule K such that K + Y = P implies that the submodule Y is P (P, then, is a projective cover of P/K (Definition 4 in this section)) and we define the submodule X of P by

Our main result states that up to isomorphism P/X is the maximal co-rational extension over P/K (by P/K, in the more precise wording of the title).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 953 - 962
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Bass, Hyman, Finitistic dimension and a homological generalization of semiprimary rings, Trans. Amer. Math. Soc., 95 (1960), 466–488.Google Scholar
2. Eckmann, B. and Schopf, A., Über injektive Moduln, Arch. Math., 4 (1953), 75–78.Google Scholar
3. Wong, E. T. and Johnson, R. E., Self-injective rings, Can. Math. Bull., 2 (1959), 167–174.Google Scholar