Abstract
AbstractWe give a group structure on unimodular rows of length three over a two-dimensional ring. This is done as follows: we take two unimodular rows take their Euler classes add these in the Euler class group and take as the sum of the unimodular rows the unimodular row whose Euler class is the sum of these two classes. We use the theory of 1-cocycles to prove that this gives a group structure on the set of unimodular rows of length three. This provides a different way of looking at the results of Vaserstein and the Vaserstein symbol.KeywordsGroupProjective moduleUnimodular rowCompletable unimodular rowCocyle2010 Mathematics Subject Classification13C1037H0558E40
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