Geodesic
Orderings and preorderings in rings with involution
Colloquium Mathematicum, Tome 83 (2000) no. 1, pp. 15-20

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DOI

The notions of a preordering and an ordering of a ring R with involution are investigated. An algebraic condition for the existence of an ordering of R is given. Also, a condition for enlarging an ordering of R to an overring is given. As for the case of a field, any preordering of R can be extended to some ordering. Finally, we investigate the class of archimedean ordered rings with involution. 
Ismail Idris. Orderings and preorderings in rings with involution. Colloquium Mathematicum, Tome 83 (2000) no. 1, pp. 15-20. doi: 10.4064/cm-83-1-15-20
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