Abstract
This article studies intrinsic or natural partial orders on involutive division rings (D,*, II), where (a + b)* = a* + b*, (ab)* = b*a*, a** = a for a, b ∈ D, and where II is the strictly positive cone for an additive partial group order on (D, +). The involution defines several natural multiplicative subgroups G ⊂ D\ 0, and the positive cones are defined by II = G +, where G + consists of all the finite sums of elements of G.
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