Background
Hazewinkel, Michiel was born on June 22, 1943 in Amsterdam, Netherlands. Son of Jan Hazewinkel and Geertrude Hendrika Werner.
(This book is a comprehensive treatment of the theory of f...)
This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.
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(Accosiative rings and algebras are very interesting algeb...)
Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample,namelythequaternions,createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative"numbersystem". During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low-dimensional algebras, division algebras, and commutative algebras, were classi?ed and characterized. The ?rst complete results in the structure theory of associative algebras over the real and complex ?elds were obtained by T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite dimensional semisimple algebras over arbitrary ?elds. Twenty years later, E.Artin proved a structure theorem for rings satisfying both the ascending and descending chain condition which generalized Wedderburn structure theorem. The Wedderburn-Artin theorem has since become a corn- stone of noncommutative ring theory. The purpose of this book is to introduce the subject of the structure theory of associative rings. This book is addressed to a reader who wishes to learn this topic from the beginning to research level. We have tried to write a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and related structures and will be accessible for independent study.
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(The main goal of this book is to present an introduction ...)
The main goal of this book is to present an introduction to and applications of the theory of Hopf algebras. The authors also discuss some important aspects of the theory of Lie algebras. The first chapter can be viewed as a primer on Lie algebras, with the main goal to explain and prove the Gabriel-Bernstein-Gelfand-Ponomarev theorem on the correspondence between the representations of Lie algebras and quivers; this material has not previously appeared in book form. The next two chapters are also "primers" on coalgebras and Hopf algebras, respectively; they aim specifically to give sufficient background on these topics for use in the main part of the book. Chapters 4-7 are devoted to four of the most beautiful Hopf algebras currently known: the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups (although these two are isomorphic, they are very different in the aspects they bring to the forefront), the Hopf algebras of the nonsymmetric and quasisymmetric functions (these two are dual and both generalize the previous two), and the Hopf algebra of permutations. The last chapter is a survey of applications of Hopf algebras in many varied parts of mathematics and physics. Unique features of the book include a new way to introduce Hopf algebras and coalgebras, an extensive discussion of the many universal properties of the functor of the Witt vectors, a thorough discussion of duality aspects of all the Hopf algebras mentioned, emphasis on the combinatorial aspects of Hopf algebras, and a survey of applications already mentioned. The book also contains an extensive (more than 700 entries) bibliography.
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mathematician university professor
Hazewinkel, Michiel was born on June 22, 1943 in Amsterdam, Netherlands. Son of Jan Hazewinkel and Geertrude Hendrika Werner.
Born in Amsterdam to January Hazewinkel and Geertrude Hendrika Werner, Hazewinkel studied at the University of Amsterdam. He received his Bachelor in Mathematics and Physics in 1963, his Master of Arts in Mathematics with a minor in Philosophy in 1965 and his Doctor of Philosophy in 1969 under supervision of Frans Oort and Albert Menalda for the thesis "Maximal Abelian Extensions of Local Fields". From 1973 to 1975 he was also Professor at the Universitaire Instelling Antwerpen, were Marcel van de Vel was his Doctor of Philosophy student.
After graduation Hazewinkel started his academic career as Assistant Professor at the University of Amsterdam in 1969. In 1970 he became Associate Professor at the Erasmus University Rotterdam, where in 1972 he was appointed Professor of Mathematics at the Econometric Institute. Here he was thesis advisor of Roelof Stroeker (1975), M. van de Vel (1975), Jo Ritzen (1977), and Gerard van der Hoek (1980).
From 1982 to 1985 he was appointed part-time Professor Extraordinarius in Mathematics at the Erasmus Universiteit Rotterdam, and part-time Head of the Department of Pure Mathematics at the Centre for Mathematics and Computer (CWI) in Amsterdam.
In 1985 he was also appointed Professor Extraordinarius in Mathematics at the University of Utrecht, where he supervised the promotion of Frank Kouwenhoven (1986), Huib-January Imbens (1989), J. Scholma (1990) and F. Wainschtein (1992). At the Centre for Mathematics and Computer CWI in Amsterdam in 1988 he became Professor of Mathematics and head of the Department of Algebra, Analysis and Geometry until his retirement in 2008.
Hazewinkel has been managing editor for journals as Nieuw Archief voor Wiskunde since 1977. Foreign Acta Applicandae Mathematicae since its foundation in 1983.
And associate editor for Chaos, Solitons & Fractals since 1991.
He was managing editor for the book series Mathematics and Its Applications for Kluwer Academic Publishers in 1977. Mathematics and Geophysics for Reidel Publishing in 1981. Encyclopedia of Mathematics for Kluwer Academic Publishers from 1987 to 1994.
And Handbook of Algebra in 9 volumes for Elsevier Science Publishers in 1995.
(This book is a comprehensive treatment of the theory of f...)
(The main goal of this book is to present an introduction ...)
(Accosiative rings and algebras are very interesting algeb...)
Member Institute of Electrical and Electronics Engineers, International Academy Computer Science and Systems, London Mathematics Society, Italian Mathematics Union, American Mathematics Society, Mathematics Association American, Japan Mathematics Society, Society Mathematics France, German Mathematics Society, New York Academy of Sciences, American Physical Society, European Physical Society, European Mathematics Society, numerous other international mathematics and physics orgns.
Married M.T. de Jong, September 10, 1969 (divorced 1990). Children: Maarten M., Annette A. Married Dausa Zvirenaite, March 8, 1991.
Children: Jan-Algimantas, Audinga-Dea.