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A Note on Injective Modules Over a d.g. Near-Ring

Published online by Cambridge University Press:  20 November 2018

A. Oswald
A. Oswald*
Affiliation:
Department of Mathematics and Statistics, Teeside Polytechnic, Middlesbrough, ClevelandU.K.
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In [3] an attempt was made at proving the following result:

(A) An N-module M over a d.g. near-ring is injective if and only if for each right ideal u of N and each N-homomorphism f:u→M there exists an element mϵM with f(a) = ma for all aϵu.

In this note we present two examples. The first is a counterexample to (A) and the second illustrates one point at which the attempt made in [3] fails.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 267 - 269
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Fröhlich, A., Distributively Generated near-rings (II Representation Theory) Proc. L.M.S. (3) (8) (1958), 95-108.Google Scholar
2. Jans, J. P., Rings and Homology, Holt, Rinehart and Winston, 1964.Google Scholar
3. Seth, V. and Tewari, K., On infective near-ring modules, Canad. Math. Bull. Vol. 17 (1974), 137-141.Google Scholar
4. Scott, W. R., Group Theory, Englewood Cliffs N.J.: Prentice-Hall, 1964.Google Scholar