  Here we try to distinguish and compare different notions of real closedness
mainly one developed by N. Schwartz in his Habilitationschrift and the other
developed by A. Sankaranand K. Varadarajan which we shall call real closed *.
We stick to the definition of real closed rings as defined and characterized N.
Schwartz and we try to determine and characterize real closed rings that are
real closed *. The main result is that real closed rings have unique real
closure * and that real closure of real closed * rings arent necessarily real
closed *.
