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Example of an Injective Module which is Not Nice

Published online by Cambridge University Press:  20 November 2018

Gerhard O. Michler
Gerhard O. Michler*
Affiliation:
Untversität Tübingen, West Germany
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In [1] Lambek calls the injective R-module I nice if every torsionfree factor module of the ring of quotients Q of R with respect to lis divisible. If lis nice then g is a dense subring of the bicommutator BicRI of I with respect to the finite topology (see [1, Proposition 2]). We now give an example of an injective R-module over an Artinian ring R which is not nice. Since R is Artinian, Q=BicRI, by Proposition B of [1].

Before we give the example, we state the following, which depends on [2] for terminology.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 133 - 134
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Lambek, J., Bicommutators of nice infectives, J. Algebra (to appear).Google Scholar
2. Lambek, J. and Michler, G., The torsion theory at a prime ideal of a right Noetherian ring, (submitted for publication).Google Scholar
3. Lambek, J., Torsion theories, additive semantics and rings of quotients, Springer Lecture Note in Math. 177, 1971.Google Scholar