Partially ordered rings and semi-algebraic geometry
نویسندگان
چکیده
منابع مشابه
Division closed partially ordered rings
Fuchs [6] called a partially-ordered integral domain, say D, division closed if it has the property that whenever a > 0 and ab > 0, then b > 0. He showed that if D is a lattice-ordered division closed field, then D is totally ordered. In fact, it is known that for a lattice-ordered division ring, the following three conditions are equivalent: a) squares are positive, b) the order is total, and ...
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In this work we attempt to generalize our result in [6] [7] for real rings (not just von Neumann regular real rings). In other words we attempt to characterize and construct real closure ∗ of commutative unitary rings that are real. We also make some very interesting and significant discoveries regarding maximal partial orderings of rings, Baer rings and essentail extension of rings. The first ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1983
ISSN: 0001-8708
DOI: 10.1016/0001-8708(83)90010-5