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Book Information:

Authors: Dmitry S. Kaliuzhnyi-Verbovetskyi and Victor Vinnikov
Title: Foundation of free noncommutative function theory
Additional book information: Mathematical Surveys and Monographs, Vol. 199, American Mathematical Society, Providence, Rhode Island, 2014, vi+183 pp., ISBN 978-1-4704-1697-3, US $77.00

E. Artin, Geometric algebra, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. Reprint of the 1957 original; A Wiley-Interscience Publication. MR 1009557, DOI 10.1002/9781118164518

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Helmer Aslaksen, Quaternionic determinants, Math. Intelligencer 18 (1996), no. 3, 57–65. MR 1412993, DOI 10.1007/BF03024312

Jean Berstel and Christophe Reutenauer, Rational series and their languages, EATCS Monographs on Theoretical Computer Science, vol. 12, Springer-Verlag, Berlin, 1988. MR 971022, DOI 10.1007/978-3-642-73235-5

Tom Bridgeland, Derived categories of coherent sheaves, International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 563–582. MR 2275610

P. M. Cohn, Free ideal rings and localization in general rings, New Mathematical Monographs, vol. 3, Cambridge University Press, Cambridge, 2006. MR 2246388, DOI 10.1017/CBO9780511542794

Alain Connes, Noncommutative geometry, Academic Press, Inc., San Diego, CA, 1994. MR 1303779

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A. Heyting, Die Theorie der linearen Gleichungen in einer Zahlenspezies mit nichtkommutativer Multiplikation, Math. Ann. 98 (1928), no. 1, 465–490 (German). MR 1512415, DOI 10.1007/BF01451604

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Maxim Kontsevich, Formal (non)commutative symplectic geometry, The Gel′fand Mathematical Seminars, 1990–1992, Birkhäuser Boston, Boston, MA, 1993, pp. 173–187. MR 1247289

Louis Halle Rowen, Polynomial identities in ring theory, Pure and Applied Mathematics, vol. 84, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR 576061

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Joseph L. Taylor, Functions of several noncommuting variables, Bull. Amer. Math. Soc. 79 (1973), 1–34. MR 315446, DOI 10.1090/S0002-9904-1973-13077-0

D. V. Voiculescu, K. J. Dykema, and A. Nica, Free random variables, CRM Monograph Series, vol. 1, American Mathematical Society, Providence, RI, 1992. A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. MR 1217253, DOI 10.1090/crmm/001

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Review Information:

Reviewer: Vladimir Retakh
Affiliation: Department of Mathematics, Rutgers University
Email: vretakh@math.rutgers.edu