COORDINATE SETS OF GENERALIZED GALOIS RINGS
Santos Manuel Coronas González, Consuelo Martı́nez, I. F. Rúa, Viktor Timofeevich Markov, Alexander A. Nechaev · Journal of Algebra and Its Applications · 2004
A Generalized Galois Ring (GGR) S is a finite nonassociative ring with identity of characteristic pn, for some prime number p, such that its top-factor [Formula: see text] is a semifield. It is well-known that if S is an associative Galois Ring (GR), then it contains a multiplicatively closed subset isomorphic to [Formula: see text], the so-called Teichmüller Coordinate Set (TCS). In this paper we show that the existence of a TCS characterizes GR in the class of all GGR S such that the multiplicative loop [Formula: see text] is right (or left) primitive.