國立高雄大學圖資館 |

Field arithmetic

Record Type:	Electronic resources : Monograph/item
Title/Author:	Field arithmeticby Michael D. Fried, Moshe Jarden.
Author:	Fried, Michael D.
other author:	Jarden, Moshe.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	xxxi, 827 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Algebraic fields.
Online resource:	https://doi.org/10.1007/978-3-031-28020-7
ISBN:	9783031280207$q(electronic bk.)

Field arithmetic
Fried, Michael D.

Field arithmetic[electronic resource] /by Michael D. Fried, Moshe Jarden. - Fourth edition. - Cham :Springer Nature Switzerland :2023. - xxxi, 827 p. :ill., digital ;24 cm. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,v. 112197-5655 ;. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,v. 11..

This book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois theory, profinite groups, algebraic function fields in one variable and plane curves. It provides complete and elementary proofs of the Chebotarev density theorem and the Riemann hypothesis for function fields, together with material on ultraproducts, decision procedures, the elementary theory of algebraically closed fields, undecidability and nonstandard model theory, including a nonstandard proof of Hilbert's irreducibility theorem. The focus then turns to the study of pseudo algebraically closed (PAC) fields, related structures and associated decidability and undecidability results. PAC fields (fields K with the property that every absolutely irreducible variety over K has a rational point) first arose in the elementary theory of finite fields and have deep connections with number theory. This fourth edition substantially extends, updates and clarifies the previous editions of this celebrated book, and includes a new chapter on Hilbertian subfields of Galois extensions. Almost every chapter concludes with a set of exercises and bibliographical notes. An appendix presents a selection of open research problems. Drawing from a wide literature at the interface of logic and arithmetic, this detailed and self-contained text can serve both as a textbook for graduate courses and as an invaluable reference for seasoned researchers.

ISBN: 9783031280207$q(electronic bk.)

Standard No.: 10.1007/978-3-031-28020-7doiSubjects--Topical Terms:

189736
Algebraic fields.

LC Class. No.: QA247

Dewey Class. No.: 512.3

Field arithmetic
LDR:02632nmm a2200337 a 4500 001 647106
003 DE-He213
005 20230612142443.0
006 m d
007 cr nn 008maaau
008 240116s2023 sz s 0 eng d
020 $a 9783031280207$q(electronic bk.)
020 $a 9783031280191$q(paper)
024 7 $a 10.1007/978-3-031-28020-7 $2 doi
035 $a 978-3-031-28020-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA247
072 7 $a PBF $2 bicssc
072 7 $a MAT002000 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.3 $2 23
090 $a QA247 $b .F899 2023
100 1 $a Fried, Michael D. $3 277749
245 1 0 $a Field arithmetic $h [electronic resource] / $c by Michael D. Fried, Moshe Jarden.
250 $a Fourth edition.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2023.
300 $a xxxi, 827 p. : $b ill., digital ; $c 24 cm.
490 1 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, $x 2197-5655 ; $v v. 11
520 $a This book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois theory, profinite groups, algebraic function fields in one variable and plane curves. It provides complete and elementary proofs of the Chebotarev density theorem and the Riemann hypothesis for function fields, together with material on ultraproducts, decision procedures, the elementary theory of algebraically closed fields, undecidability and nonstandard model theory, including a nonstandard proof of Hilbert's irreducibility theorem. The focus then turns to the study of pseudo algebraically closed (PAC) fields, related structures and associated decidability and undecidability results. PAC fields (fields K with the property that every absolutely irreducible variety over K has a rational point) first arose in the elementary theory of finite fields and have deep connections with number theory. This fourth edition substantially extends, updates and clarifies the previous editions of this celebrated book, and includes a new chapter on Hilbertian subfields of Galois extensions. Almost every chapter concludes with a set of exercises and bibliographical notes. An appendix presents a selection of open research problems. Drawing from a wide literature at the interface of logic and arithmetic, this detailed and self-contained text can serve both as a textbook for graduate courses and as an invaluable reference for seasoned researchers.
650 0 $a Algebraic fields. $3 189736
650 0 $a Algebraic number theory. $3 190879
650 1 4 $a Algebra. $3 188312
650 2 4 $a Mathematics. $3 184409
650 2 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Field Theory and Polynomials. $3 274058
650 2 4 $a Geometry. $3 183883
650 2 4 $a Mathematical Logic and Foundations. $3 274479
700 1 $a Jarden, Moshe. $3 256421
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, $v v. 11. $3 956327
856 4 0 $u https://doi.org/10.1007/978-3-031-28020-7
950 $a Mathematics and Statistics (SpringerNature-11649)