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020 _a9783662679746
_9978-3-662-67974-6
024 7 _a10.1007/978-3-662-67974-6
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
100 1 _aHien, Marco.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981976
245 1 0 _aAbstract Algebra
_h[electronic resource] :
_bSuitable for Self-Study or Online Lectures /
_cby Marco Hien.
250 _a1st ed. 2024.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2024.
300 _aIX, 307 p. 140 illus., 2 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematics Study Resources,
_x2731-3832 ;
_v7
505 0 _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.
520 _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.
650 0 _aAlgebra.
_91501
650 1 4 _aAlgebra.
_91501
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662679739
776 0 8 _iPrinted edition:
_z9783662679753
830 0 _aMathematics Study Resources,
_x2731-3832 ;
_v7
_981153
856 4 0 _uhttps://doi.org/10.1007/978-3-662-67974-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c62273
_d62273