Abstract:In {A class of simple Moufang loops}, Proc. Amer. Math. Soc. {7} (1956), 471--482, Paige used the vector matrix construction over fields to produce simple Moufang loops. The purpose of this paper is to generalize the construction to the class of commutative rings, and examine the Moufang loops arising in this fashion. Specific attention is paid to the construction over the ring of integers modulo four.
Keywords: Zorn vector matrix, Moufang loop, Paige loop
AMS Subject Classification: 20N05