02657nam a22004695i 4500 978-3-030-32796-5 DE-He213 20200904104947.0 cr nn 008mamaa 200713s2020 gw | s |||| 0|eng d 9783030327965 978-3-030-32796-5 10.1007/978-3-030-32796-5 doi QA150-272 PBF bicssc MAT002000 bisacsh PBF thema 512 23 Douady, Régine. author. aut http://id.loc.gov/vocabulary/relators/aut Algebra and Galois Theories [electronic resource] / by Régine Douady, Adrien Douady. 1st ed. 2020. Cham : Springer International Publishing : Imprint: Springer, 2020. XXIII, 462 p. 33 illus., 6 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Introduction -- Chapter 1. Zorn’s Lemma -- Chapter 2. Categories and Functors -- Chapter 3. Linear Algebra -- Chapter 4. Coverings -- Chapter 5. Galois Theory -- Chapter 6. Riemann Surfaces -- Chapter 7. Dessins d’Enfants -- Bibliography -- Index of Notation. Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory. Algebra. Algebra. https://scigraph.springernature.com/ontologies/product-market-codes/M11000 Douady, Adrien. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) Springer Nature eBook Printed edition: 9783030327958 Printed edition: 9783030327972 Printed edition: 9783030327989 https://doi.org/10.1007/978-3-030-32796-5 ZDB-2-SMA ZDB-2-SXMS 461199 461199