Witt Equivalence of Fields
نویسندگان
چکیده
Definition 1.1. If S is a multiplicative subset of a ring A (commutative with 1), the quotient hyperring A/mS = (A/mS,+, ·,−, 0, 1) is defined as follows: A/mS is the set of equivalence classes with respect to the equivalence relation ∼ on A defined by a ∼ b iff as = bt for some s, t ∈ S. The operations on A/mS are the obvious ones induced by the corresponding operations on A: Denote by a the equivalence class of a. Then a ∈ b + c iff as = bt + cu for some s, t, u ∈ S, ab = ab, −a = −a. Also, 0 = 0, and 1 = 1.
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