Geodesic
THE UNIT SUM NUMBER OF SOME PROJECTIVE MODULES
Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 71-74

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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 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.
DOI : 10.1017/S0017089507004041
Mots-clés : 13C10, 16D40, 16D10, 16G10, 16W20 
ASHRAFI, NAHID. THE UNIT SUM NUMBER OF SOME PROJECTIVE MODULES. Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 71-74. doi: 10.1017/S0017089507004041
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