WRITING UNITS OF INTEGRAL GROUP RINGS OF FINITE ABELIAN GROUPS AS A PRODUCT OF BASS UNITS

We give a constructive proof of the theorem of Bass and Milnor saying that if G is a finite abelian group then the Bass units of the integral group ring ZG generate a subgroup of finite index in its unit group U(ZG). Our proof provides algorithms to represent some units that contribute to only one simple component of QG and generate a subgroup of finite index in U(ZG) as product of Bass units. We also obtain a basis B formed by Bass units of a free abelian subgroup of finite index in U(ZG) and give, for an arbitrary Bass unit b, an algorithm to express b(psi(vertical bar G vertical bar)) as a product of a trivial unit and powers of at most two units in this basis B.