LEADER 03140nam 22004815 450 001 9910879590503321 005 20240807101726.0 010 $a9783662679746 024 7 $a10.1007/978-3-662-67974-6 035 $a(CKB)33734536300041 035 $a(MiAaPQ)EBC31588388 035 $a(Au-PeEL)EBL31588388 035 $a(MiAaPQ)EBC31591729 035 $a(Au-PeEL)EBL31591729 035 $a(DE-He213)978-3-662-67974-6 035 $a(EXLCZ)9933734536300041 100 $a20240806d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAbstract Algebra $eSuitable for Self-Study or Online Lectures /$fby Marco Hien 205 $a1st ed. 2024. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2024. 215 $a1 online resource (310 pages) 225 1 $aMathematics Study Resources,$x2731-3832 ;$v7 311 08$a9783662679739 327 $aMotivation and prerequisites -- Field extensions and algebraic elements -- Groups -- Group quotients and normal divisors -- Rings and ideals -- Euclidean rings, principal ideal rings, Noetherian rings -- Factorial rings -- Quotient fields for integrality domains -- Irreducible polynomials in factorial rings -- Galois theory (I) - Theorem A and its variant A' -- Intermezzo - explicit example -- Normal fields extensions -- Separability -- Galois theory (II) - The main theorem -- Cyclotomic fields -- Finite fields -- More group theory - Group operations and Sylow -- Resolvability of polynomial equations. 330 $aThis book contains the fundamental basics of algebra at university level. In addition to elementary algebraic structures such as groups, rings and fields, the text in particular covers Galois theory together with its applications to cyclotomic fields, finite fields as well as solving polynomial equations. Special emphasis is placed on the natural development of the contents. Various supplementary explanations support this basic idea, point out connections and help to better comprehend the underlying concepts. The book is particularly suited as a textbook for learning algebra in self-study or to accompany online lectures. The Author: Prof. Dr. Marco Hien worked at the University of Regensburg after a postdoctoral year at the University of Chicago. Since 2010, he has been Professor of Algebra and Number Theory at the University of Augsburg with research interests in algebraic geometry and algebraic analysis. In 2020, he received the "Prize for Good Teaching" from the Bavarian Ministry of Science. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content. 410 0$aMathematics Study Resources,$x2731-3832 ;$v7 606 $aAlgebra 606 $aAlgebra 615 0$aAlgebra. 615 14$aAlgebra. 676 $a512.02 700 $aHien$b Marco$01765224 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910879590503321 996 $aAbstract Algebra$94206651 997 $aUNINA