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The n-insertive subgroups of units

Published online by Cambridge University Press:  17 April 2009

David Dolžn
David Dolžn
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia
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Let R be a finite ring. Let us denote its group of units by G = G(R) and its Jacobson radical by J = J(R). Let n be an arbitrary integer. We prove that R is an n-insertive ring if and only if G is an n-insertive group and show that every n-insertive finite ring is a direct sum of local rings. We prove that if n is a unit, then the local ring R is n-insertive if and only if its Jacobson group 1 + J is n-insertive and find an example to show that this is not true if n is a non-unit.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 1 , February 2007 , pp. 23 - 26
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Cohen, J.-A. and Koh, K., ‘The group of units in a compact ring’, J. Pure Appl. Algebra 54 (1988), 167–179.CrossRefGoogle Scholar
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[3]Xu, L.Q. and Xue, W.M., ‘Minimal non-commutative n-insertive rings’, Acta Math. Sin. (Engl. Ser.) 19 (2003), 141–146.CrossRefGoogle Scholar