Units in alternative loop rings (Q1076788)

Several results concerning units in integral group rings are generalized to the alternative case. Among others, the following interesting theorem is proved: Let \(L\) be a periodic Moufang loop such that the integral loop ring \(ZL\) is alternative. Then every central unit in \(ZL\) is trivial, i.e. belongs to \(L\cup -L\), iff the centre of \(L\) and the factor \(L/L'\) are abelian groups of exponent \(\in \{2,3,4,6\}\).