# formally real field

## Primary tabs

Defines:
formally real, real closed, real closure
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### formally real fields are fields that are real rings

Maybe you should add an alternative "definition" or a remark.

A formally real field is just a field that is a real ring.

And that formally real fields are also known as real fields... I will add to my real rings a sentence that this ring is also called a "formally real ring".

The usage of the word "formally" was done earlier (the earliest excerpt I have seen was from a paper I saw from Tarski and one from Erdos.. or maybe both of them had written the same paper.. I have a bad memory). And then sometime later it just got too tedious to write formally real fields, so people dropped the "formally" part. But still a lot of mathematician do write "formally".