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Edited by: William B. Jacob, University of California, Santa Barbara, CA, Tsit-Yuen Lam, University of California, Berkeley, CA, and Robert O. Robson, Oregon State University, Corvallis, OR
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Contemporary Mathematics
1994; 405 pp; softcover
Volume: 155
ISBN-10: 0-8218-5154-3
ISBN-13: 978-0-8218-5154-8
List Price: US$50 Member Price: US$40
Order Code: CONM/155

The papers in this volume grew out of a year-long program in "Real Algebraic Geometry and Quadratic Forms", held at the University of California at Berkeley during the 1990-1991 academic year. This valuable collection of research articles by top workers serves as a record of current developments in these areas and as a tribute to the fruitful interaction between them. Students and researchers alike will find this book a useful reference, with articles ranging from the technical to the expository. Also included are summaries of the current developments in several sub-disciplines and indications of new research directions.

Graduate students and researchers in computational algebra and applications of real algebraic geometry.

• T. Recio and C. Andradas -- D. W. Dubois and the pioneer days of real algebraic geometry
• Papers on real algebraic geometry
• S. Akbulut -- On algebraic structures of manifolds
• C. Andradas and J. M. Ruiz -- On local uniformization of orderings
• R. Berr -- Real algebraic geometry over $$p$$-real closed fields
• L. Bröcker -- On the reduction of semialgebraic sets by real valuations
• T. C. Craven -- Orderings for noncommutative rings
• C. N. Delzell -- Nonexistence of analytically varying solutions to Hilbert's 17th problem
• M. A. Dickmann -- A combinatorial geometric structure on the space of orders of a field II
• M. J. González-Lopez and T. Recio -- Formal determination of polynomial consequences of real orthogonal matrices
• R. Huber and M. Knebusch -- On valuation spectra
• M. Marshall -- Minimal generation of basic sets in the real spectrum of a commutative ring
• A. Pfister -- A new proof of the homogeneous nullstellensatz for $$p$$-fields, and applications to topology
• M. J. de la Puente -- The compatible valuation rings of the coordinate ring of the real plane
• G. Stengle -- Estimates for parametric nonuniformity in representations of a definite polynomial as a sum of fourth powers
• M. Krüskemper -- On annihilators in graded Witt rings and in Milnor's $$K$$-theory
• D. B. Leep and A. S. Merkurjev -- Growth of the $$u$$-invariant under algebraic extensions
• J. Mináč -- Remarks on Merkurjev's investigations of the $$u$$-invariant