Convex Extensions of Partially Ordered Rings
نویسنده
چکیده
This series of lectures is about algebraic aspects of real algebraic geometry. Partially ordered rings (porings) occur very naturally in real algebraic geometry, as well as in other branches of mathematics. There is a rich classical theory of porings (the beginnings dating back to the 1930s and 1940s). To a large extent it was inspired by the study of rings of continuous functions in analysis and topology. I will mention rings of continuous functions from time to time, but will not attempt an in-depth discussion. With the rise of real algebraic geometry in the last 25 years there also arose a need for algebraic methods that are specifically adapted to real algebraic geometry, as opposed to general algebraic geometry. For a long time commutative algebra has been the answer to a similar need in general algebraic geometry. For real algebraic geometry, an important part of the answer is the theory of porings. However, the classical theory of porings frequently does not address the questions from real algebraic geometry. Therefore it is necessary to develop a more comprehensive theory of porings that includes rings of continuous functions, but also deals with phenomena occurring in real geometry. This is a major task that is not nearly finished at the present time. First I give the definition of porings:
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تاریخ انتشار 2005