Department of Mathematics
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It is well-known that the class of all groups which are multiplicative groups of fields has no first order characterization. However, there are several theorems which use as little as possible of additive properties to represent the given group as the multiplicative group of a field (or a division ring). The so-called rational identities (of Amitsur, Hua, Cohn and Klein, to name a few) are some of the well-known examples of such properties. In this talk, we prove one such representation theorem by using the unary operation \( f(y) = 1- y \) and develop enough properties of this unary term to eventually obtain an embedding theorem for the given group.

REFERENCES:

1. Emil Artin, Geometric Algebras
2. P. M. Cohn, Skew Fields