Whitehead groups of exchange rings with primitive factors artinian

Huanyin Chen and Fu-an Li

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 26, 1-6

Abstract:

We show that if R is an exchange ring with primitive factors artinian then K 1 ( R ) ≅ U ( R ) / V ( R ) , where U ( R ) is the group of units of R and V ( R ) is the subgroup generated by { ( 1 + a b ) ( 1 + b a ) − 1 | a , b ∈ R       with       1 + a b ∈ U ( R ) } . As a corollary, K 1 ( R ) is the abelianized group of units of R if 1 / 2 ∈ R .

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:295643

DOI: 10.1155/S0161171201005464

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