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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 \(K_1\)