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THE UNIT SUM NUMBER OF SOME PROJECTIVE MODULES

Published online by Cambridge University Press:  01 January 2008

NAHID ASHRAFI
NAHID ASHRAFI*
Affiliation:
Department of Mathematics, Semnan University, Semnan, Iran e-mail: ,
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Abstract

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The unit sum number u(R) of a ring R is the least k such that every element is the sum of k units; if there is no such k then u(R) is ω or ∞ depending whether the units generate R additively or not. If RM is a left R-module, then the unit sum number of M is defined to be the unit sum number of the endomorphism ring of M. Here we show that if R is a ring such that R/J(R) is semisimple and $\Z_{2}$ is not a factor of R/J(R) and if P is a projective R-module such that JP ≪ P, (JP small in P), then u(P)= 2. As a result we can see that if P is a projective module over a perfect ring then u(P)=2.

Keywords

13C1016D4016D1016G1016W20

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 1 , January 2008 , pp. 71 - 74
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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