Universal Localization and Group Cohomology
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Date
2006-08-10
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Virginia Tech
Abstract
Two results are obtained in this work. First, we prove that for a commutative ring embedded in a larger ring, which is not necessarily commutative, its division and rational closures coincide.
Second, for an infinite discrete group G, we investigate group cohomology and homology with coefficients in lp(G). We prove that if G is of type FPn, then all its homology and cohomology groups up to n are either zero or infinite dimensional. This generalizes one of the results obtained by Bekka and Valette
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Keywords
Rational Closure, Division Closure, Group Cohomology, Universal Localization