A CAYLEY THEOREM FOR THE MULTIPLICATIVE SEMIGROUP OF A FIELD
E. Nazari, Yuri Movsisyan · Journal of Algebra and Its Applications · 2011
Since there exist two commutative elementarily equivalent semigroups of which one is the multiplicative semigroup of a field and the other is not a multiplicative semigroup of any field, it is impossible to characterize multiplicative semigroups of fields by formulas of the first order language (logic). In this work we characterize the multiplicative semigroup of a field by its binary representation (Cayley type theorem).