By Bruce A. Magurn
This e-book is either an advent to K-theory and a textual content in algebra. those roles are solely appropriate. at the one hand, not anything greater than the elemental algebra of teams, earrings, and modules is required to give an explanation for the clasical algebraic K-theory. nevertheless, K-theory is a traditional organizing precept for a standard themes of a moment path in algebra, and those issues are awarded rigorously the following. The reader won't in basic terms research algebraic K-theory, but additionally Dedekind domain names, type teams, semisimple earrings, personality concept, quadratic kinds, tensor items, localization, crowning glory, tensor algebras, symmetric algebras, external algebras, relevant easy algebras, and Brauer teams. The presentation is self-contained, with the entire priceless historical past and proofs, and is split into brief sections with workouts to augment the information and recommend extra traces of inquiry. the must haves are minimum: only a first semester of algebra (including Galois conception and modules over a relevant excellent domain). No adventure with homological algebra, research, geometry, quantity conception, or topology is thought. the writer has successfuly used this article to educate algebra to first 12 months graduate scholars. chosen subject matters can be utilized to build quite a few one-semester classes; insurance of the full textual content calls for an entire yr.
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