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In mathematics a Steinberg symbol is a pairing function which generalises the Hilbert symbol and plays a role in the algebraic K-theory of fields. It is named after mathematician Robert Steinberg.
For a field F we define a Steinberg symbol to be a function : F ∗ × F ∗ → G {\displaystyle :F^{*}\times F^{*}\rightarrow G} , where G is an abelian group, written multiplicatively, such that
The symbols on F derive from a "universal" symbol, which may be regarded as taking values in F ∗ ⊗ F ∗ / ⟨ a ⊗ 1 − a ⟩ {\displaystyle F^{*}\otimes F^{*}/\langle a\otimes 1-a\rangle }. By a theorem of Matsumoto, this group is K 2 F {\displaystyle K_{2}F} and is part of the Milnor K-theory for a field.