Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T08:57:08.066Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Non-Existence of Injective Near-Ring Modules

Published online by Cambridge University Press:  20 November 2018

Bernhard Banaschewski  and
Evelyn Nelson
Bernhard Banaschewski
Affiliation:
Department of Mathematics McMasterUniversity Hamilton, Ont.CanadaL8S 4K1
Evelyn Nelson
Affiliation:
Department of Mathematics McMasterUniversity Hamilton, Ont.CanadaL8S 4K1
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.

Associated with any near-ring R, and any set S of distributive elements of R, one has a natural notion of S-distributive R-modules, analogous to that of modules over rings and including the latter as special case (Frohlich [6]; we recall the details in Section 1). Since near-rings can be viewed as slightly deficient rings, it makes sense to enquire whether such near-ring modules share with modules over rings the familiar and important property of having injective hulls.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 17 - 23
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Banaschewski, B., Injectivity and Essential Extensions in Equational Classes of Algebras. Proc. Conference on Universal Algebra (1969) Queen's Series in Pure and Applied Mathematics No. 25, Kingston, Ontario 1970.Google Scholar
2. Banaschewski, B. and Nelson, E., Equational Compactness in Equational Classes of Algebras. Alg. Univ. 2 (1972), 152-165.Google Scholar
3. Beidleman, J. C., Quasi-regularity in near-rings. Math. Zeit. 89 (1965), 224-229.Google Scholar
4. Boone, W. W. and Higman, G., An algebraic characterization of groups with soluble word problem. J. Aust. Math. Soc. 18 (1974), 41-53.Google Scholar
5. Fröhlich, A., Distributively generated Near-Rings I and II. Proc. London Math. Soc. 8 (1958), 76-108.Google Scholar
6. Fröhlich, A., On Groups over a d.g. near-ring (I), Quart, J. Math. 11 (1960), 193-210.Google Scholar
7. Jacobson, N., The Theory of Rings. New York. 1943.Google Scholar
8. Oswald, A., A note on injective modules over a d.g. near-ring. Canadian Math. Bull, (in print)Google Scholar
9. Seth, V. and Tewari, K., On injective near-ring modules. Can. Math. Bull. 17 (1974), 137-142.Google Scholar
10. Taylor, W., Residually small varieties. Alg. Univ. 2 (1972), 33-53.Google Scholar