A Note on Sinnottʹs Definition of Circular Units of an Abelian Field Original Research Article

This note deals with a slight change of Sinnottʹs definition of circular units of an abelian field. The reason for this new definition giving a bigger group of units is as follows. Sinnottʹs formula for the index of circular units in the full group of units contains two factors which are difficult to handle: the index of the Sinnott module and (in the case of an imaginary field) an unknown power of 2. If we use the mentioned definition, the power of 2 in the corresponding formula can be easily described.