Real Closed Rings and Real Closed * Rings

Details Real Closed Rings and Real Closed * Rings Real Closed Rings and Real Closed * Rings

2007-07-15

arxiv.org/abs/0707.2189v2

Mathematics

Rings and Algebras

Scientific paper

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 *.

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