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Full subrings of E-rings

Published online by Cambridge University Press:  17 April 2009

Shalom Feigelstock
Shalom Feigelstock
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, Ramat Gan 52900, Israel
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Abstract

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A ring R is said to be an E-ring if the map R → of E (R)+ into the ring of endomorphisms of its additive group via a ↪ al = left multiplication by a, is an isomorphism. In this note torsion free rings R for which the group Rl, of left multiplication maps by elements of R, is a full subgroup of E(R)+ will be considered. These rings are called TE-rings. It will be shown that TE-rings satisfy many properties of E-rings, and that unital TE-rings are E-rings. If R is a TE-ring, then E(R+) is an E-ring, and E(R+)+ / is bounded. Some results concerning additive groups of TE-rings will be obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 2 , October 1996 , pp. 275 - 280
Copyright
Copyright © Australian Mathematical Society 1996

References

REFERENCES

[1]Bowshell, R.A. and Schultz, P., ‘Unital rings whose additive endomorphisms commute’, Math. Ann. 228 (1977), 197–214.CrossRefGoogle Scholar
[2]Feigelstock, S., Additive groups of rings, Research Notes in Mathematics 83 (Pitman, London, 1983).Google Scholar
[3]Feigelstock, S., ‘E-associative rings’, Canad. Math. Bull. 36 (1993), 147–153.CrossRefGoogle Scholar
[4]Fuchs, L., Abelian groups 1 (Academic Press, New York, London, 1970).Google Scholar
[5]Fuchs, L., Abelian groups 2 (Academic Press, New York, London, 1973).Google Scholar
[6]Pierce, R., ‘E-modules’, Contemp. Math. 87 (1989), 221–240.CrossRefGoogle Scholar
[7]Schultz, P., ‘The endomorphism ring of the additive group of a ring’, J. Austral. Math. Soc. 15 (1973), 60–69.CrossRefGoogle Scholar