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Ordered algebraic structures --- Geometry --- 51 --- Mathematics --- Hjelmslev planes. --- Skew fields. --- 51 Mathematics
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The first half of the book is a general study of homomorphisms to simple artinian rings; the techniques developed here should be of interest to many algebraists. The second half is a more detailed study of special types of skew fields which have arisen from the work of P. M. Cohn and the author. A number of questions are settled; a version of the Jacobian conjecture for free algebras is proved and there are examples of skew field extensions of different but finite left and right dimension.
Commutative rings. --- Representations of rings (Algebra) --- Skew fields. --- s-fields --- Algebraic fields --- Rings (Algebra) --- Ordered algebraic structures --- Representations of rings (Algebra).
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The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. This material is presented in a classical, though unusual, way. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments in the theory which, until now, have not been available except in journals. The principal topic discussed in this section is reduced K,-theory. This book will be of interest to graduate students in pure mathematics and to professional mathematicians.
Skew fields. --- Brauer groups. --- K-theory. --- Algebraic topology --- Homology theory --- Brauer group --- Groups, Brauer --- Associative algebras --- s-fields --- Algebraic fields --- Brauer groups --- K-theory --- Skew fields --- brauer --- enkelvoudig --- groepen --- lichaam --- producten --- ring --- scheef --- tensoren --- velden --- 512.623 --- 512 --- 512.623 General field theory --- General field theory --- 512 Algebra --- Algebra --- Algebraic fields. --- Corps algébriques. --- Ordered algebraic structures --- Algèbre --- Algèbre --- Corps algébriques.
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