Geodesic
Universal fields of fractions for polycyclic group algebras
Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 103-113

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Let G be a polycyclic-by-finite group and let K[G] denote its group algebra over the field K. In this paper we discuss localization in K[G] and in particular we prove that every faithful completely prime ideal is localizable. Furthermore, using a sequence of localizations, we show that, for G polyinfinite cyclic, the classical right quotient ring (K[G]) is in fact a universal field of fractions for K[G]. Finally we offer an example of a domain K[G] which does not have a universal field of fractions. 
Passman, D. S. Universal fields of fractions for polycyclic group algebras. Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 103-113. doi: 10.1017/S0017089500004869
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