On \(K_1\)-groups of semiperfect rings. (English) Zbl 1199.19003
Summary: In this paper, the \(K_1\)-group of a semiperfect ring is studied. By using the known result of \(K_1\)-group of a semilocal ring and the construction of the semiperfect ring. It is proved that the \(K_1\)-group of a semiperfect ring \(R\) is the quotient group of the direct sum of \(K_1\)-groups of some subrings of \(R\) by a subgroup of the unit group of \(R\).
MSC:
19B99 | Whitehead groups and \(K_1\) |