Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T21:30:47.675Z Has data issue: false hasContentIssue false
  • English
  • Français

E-Associative Rings

Published online by Cambridge University Press:  20 November 2018

Shalom Feigelstock
Shalom Feigelstock*
Affiliation:
Bar-Ilan University Ramat-Gan Israel
Rights & Permissions [Opens in a new window]

Abstract

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.

A ring R is E-associative if φ(xy) = φ(x)y for all endomorphisms φ of the additive group of R, and all x,y ∊ R. Unital E-associative rings are E-rings. The structure of the torsion ideal of an E-associative ring is described completely. The E-associative rings with completely decomposable torsion free additive groups are also classified. Conditions under which E-associative rings are E-rings, and other miscellaneous results are obtained.

Keywords

20K99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 2 , 01 June 1993 , pp. 147 - 153
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Feigelstock, S., Additive Groups of Rings, Research Notes in Mathematics 83, Pitman, London, (1983).Google Scholar
2. Fuchs, L., Infinite Abelian Groups, vol. I, Academic Press, New York-London, 1971.Google Scholar
3. Fuchs, L., Infinite Abelian Groups, vol. II, Academic Press, New York-London, 1973.Google Scholar
4. Pierce, R., E-modules, Contemporary Math. 87(1989), 221–240.Google Scholar
5. Schultz, P., Periodic homomorphism sequences of abelian groups, Arch. Math. 21(1970), 132—155.Google Scholar
6. Schultz, P., The endomorphism ring of the additive groups of a ring, J. Austral. Math. Soc. 15(1973), 60–69.Google Scholar