Real Closed Rings and Real Closed * Rings
نویسنده
چکیده
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. Sankaran and K. Varadarajan in [SV] which we shall call real closed *. We stick to the definition of real closed rings as defined and characterized in [RCR] 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 *. Unless otherwise stated all the rings in this paper are commutative unitary partially ordered rings (porings). The reader is assumed to know results in [KS] Kapitel III. Notation. Given a ring A we use SperA to mean the topological space (Harrison Topology) of all the prime cones of A such that they contain the partial ordering of A. If the partial ordering is not specifically mentioned then we will mostly assume it to be
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