Hypercentral units in alternative loop rings (Q1770504)

A Moufang loop \(L\) is an \(ZA\) loop if the integral loop ring \(ZL\) is alternative but not associative. The center, \(Z(L)\), of \(L\) consists of those elements which commute and associate with all elements of \(L\). The upper central series is defined as in group theory and the hypercenter, \(H(L)\), is the union of all members of the upper central series. The main result shows that if \(U\) is the loop of units of \(ZL\), then \(H(U)\) equals the second center and, further, \(H(U)=Z(U)\) except when the torsion subloop of \(U\) is one of two types.