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A Generalization of Divisibility and Injectivity in Modules

Published online by Cambridge University Press:  20 November 2018

D. F. Sanderson
D. F. Sanderson*
Affiliation:
Western Washington State College, BellinghamWashington
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Classically, there has been, for obvious reasons, an intimate relation between the concepts "rings of quotients" and "divisible modules". Recently, however, their generalizations have appeared to diverge.

For example, Hattori ([9]) and Levy ([15]) have generalized the concept of "divisibility" as follows: Hattori (respectively Levy) defines a left R-module M over a ring R to be divisible if and only if Ext1R(R/I, M)=0 for every principal left ideal I ⊂ R (respectively, every principal left ideal I ⊂ R which is generated by a regular element of R).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 4 , June 1965 , pp. 505 - 513
Copyright
Copyright © Canadian Mathematical Society 1965

References

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