Ring Alternative Loops and their Loop Rings

In 1983, a few examples of Moufang loops whose loop rings are alternative, but not associative, were discovered. Since that time, there has been a great deal of worle devoted to the study of such loops and to their loop rings. This paper is a survey of some of the more important results in this still relatively young area

Hypercentral units in alternative loop rings

AbstractLet L be an RA loop, that is, a loop whose loop rings are alternative, but not associative, rings (in any characteristic). We find necessary and sufficient conditions under which the hypercentral units in the integral loop ring ZL are central

Minimally nonassociative Moufang loops with a unique nonidentity commutator are ring alternative

summary:We investigate finite Moufang loops with a unique nonidentity commutator which are not associative, but all of whose proper subloops are associative. Curiously, perhaps, such loops turn out to be ``ring alternative'', in the sense that their loop rings are alternative rings