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Sets and Transfinite Algebra出版済み 3-5週間でお届けいたします。
Title: Sets and Transfinite Algebra Series: London Mathematical Society Student Texts Author: Muller, Thomas (Universitat Wien, Austria) Publisher: Cambridge University Press ISBN: 9781009737845 Cover: HARDCOVER Date: 2026年04月 こちらの商品は学校・法人様向け（機関契約）のオンラインブック版がございます。 オンラインブックの価格、納期につきましては弊社営業員または当ECサイトよりお問い合わせください。  DESCRIPTION This two-part book offers a rigorous yet accessible exploration of set theory and transfinite algebra, with a particular emphasis on the axiom of choice and its applications. Part I presents an informal axiomatic introduction to the foundations of set theory, including a detailed treatment of the axiom of choice and its equivalents, suitable for advanced undergraduates. Part II, aimed at graduate students and professional mathematicians, treats selected topics in transfinite algebra where the axiom of choice, in one form or another, is useful or even indispensable. The text features self-contained chapters for flexible use, and includes material rarely found in the literature, such as Tarski's work on complete lattices, Hamel's solution to Cauchy's functional equation, and Artin's resolution of Hilbert's 17th problem. Over 140 exercises, with full solutions provided in the Appendix, support active engagement and deeper understanding, making this a valuable resource for both independent study and course preparation. Features the first English-language exposition of Artin's solution to Hilbert's 17th problem, originally published in German Over 140 exercises with complete solutions invite readers to actively engage with the material and test their understanding Covers seldom-treated topics such as Novotny's morphism construction and Tarski's generalization of Weierstrass' theorem TABLE OF CONTENTS Part I. Set Theory: 1. The axioms of set theory 2. Correspondences, mappings, and quotient sets 3. Ordered sets 4. Around the axiom of choice 5. Cardinals and ordinals 6. First-order logic and the axioms of set theory revisited 7. Some excursions Part II. Topics in Transfinite Algebra: 8. Group and ring structures on non-empty sets 9. Orderable abelian groups and fields 10. Subdirect decomposition of algebras 11. Dependence relations, rank functions, and closure operators 12. Semisimple and injective modules 13. The Jacobson radical of a ring 14. Artin's solution of Hilbert's 17th problem 最近チェックした商品
18,631円(税1,693円)
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