標題: Titlebook: Galois Theory Through Exercises; Juliusz Brzeziński Textbook 2018 Springer International Publishing AG, part of Springer Nature 2018 Galoi [打印本頁] 作者: SPARK 時間: 2025-3-21 17:55
書目名稱Galois Theory Through Exercises影響因子(影響力)
書目名稱Galois Theory Through Exercises影響因子(影響力)學科排名
書目名稱Galois Theory Through Exercises網絡公開度
書目名稱Galois Theory Through Exercises網絡公開度學科排名
書目名稱Galois Theory Through Exercises被引頻次
書目名稱Galois Theory Through Exercises被引頻次學科排名
書目名稱Galois Theory Through Exercises年度引用
書目名稱Galois Theory Through Exercises年度引用學科排名
書目名稱Galois Theory Through Exercises讀者反饋
書目名稱Galois Theory Through Exercises讀者反饋學科排名
作者: coddle 時間: 2025-3-21 23:12 作者: 精密 時間: 2025-3-22 02:39 作者: avenge 時間: 2025-3-22 04:50
Cemal Cingi,Arzu Yorganc?o?lu,Alvaro A. Cruzalois groups of its reductions modulo prime numbers. Several exercises are concerned with Dedekind’s theorem, allowing for the construction of polynomials with given Galois groups and the solution of the inverse problem for the symmetric group S..作者: 倔強不能 時間: 2025-3-22 11:14 作者: bibliophile 時間: 2025-3-22 15:48
Separable Extensions,ove the theorem on primitive element which says that a finite separable extension can be generated over its ground field by only one element. This theorem is usually part of any standard course on the subject.作者: bibliophile 時間: 2025-3-22 18:22 作者: 起皺紋 時間: 2025-3-22 23:50
Computing Galois Groups,alois groups of its reductions modulo prime numbers. Several exercises are concerned with Dedekind’s theorem, allowing for the construction of polynomials with given Galois groups and the solution of the inverse problem for the symmetric group S..作者: Bouquet 時間: 2025-3-23 01:50
Cyclotomic Extensions,their properties, which find different applications in number theory and algebra. Among many applications, there is a proof of a special case of Dirichlet’s theorem on primes in arithmetic progression using the cyclotomic polynomials. This chapter also includes an exercise on a solution of the inverse Galois problem for all abelian groups.作者: Vulnerable 時間: 2025-3-23 08:50 作者: Oscillate 時間: 2025-3-23 12:37 作者: 壓倒 時間: 2025-3-23 15:07 作者: 頌揚本人 時間: 2025-3-23 18:44
https://doi.org/10.1007/978-1-4613-0779-2em, which gives a characterization of irreducible solvable polynomials of prime degree. Both Galois’ and Weber’s results give examples of concrete unsolvable polynomials over the rational numbers. The solvability by real radicals in connection with “casus irreducibilis” is also discussed.作者: 發(fā)酵劑 時間: 2025-3-24 00:44
Benign Tracheal/Bronchial Stenosis,rther knowledge related to Galois groups of field extensions. This chapter contains several exercises concerned with geometric straightedge-and-compass constructions. We prove two theorems: the first tends to be used in proofs of impossibility of some straightedge-and-compass constructions; the second tends to be used in proofs of possibility.作者: 信條 時間: 2025-3-24 03:11 作者: RLS898 時間: 2025-3-24 09:00
Splitting Fields,mple polynomials over finite prime fields. We further consider the notion of an algebraic closure of a field ., which is a minimal field extension of K, containing a splitting field of every polynomial with coefficients in ..作者: Emmenagogue 時間: 2025-3-24 12:46 作者: colloquial 時間: 2025-3-24 16:51
Geometric Constructions,rther knowledge related to Galois groups of field extensions. This chapter contains several exercises concerned with geometric straightedge-and-compass constructions. We prove two theorems: the first tends to be used in proofs of impossibility of some straightedge-and-compass constructions; the second tends to be used in proofs of possibility.作者: 冰雹 時間: 2025-3-24 22:29
Examples and Selected Solutions,Chap. 16). Third, some of the solutions presented in this chapter may be regarded as the last resort when serious attempts to solve a problem have been fruitless, or in order to compare one’s own solution to the one suggested in the book.作者: START 時間: 2025-3-24 23:54
Airbreathing Hypersonic Propulsioning roots applied to coefficients. We give examples of quantic equations for which such formulae exist (e.g. de Moivre’s quintics) and show that the ideas which work for equations of degrees up to 4 have no evident generalizations. We also briefly discuss “casus irreducibilis” related to cubic equations.作者: Morphine 時間: 2025-3-25 05:46
https://doi.org/10.1007/978-3-319-46729-0in the modern presentation of Galois theory. In the exercises, we find Galois groups of many field extensions and we use also use this theorem for various problems on field extensions and their automorphism groups.作者: 帶子 時間: 2025-3-25 08:04
Assessment and Clinical Patterns,e of the problems are suitably structured in order to introduce some interesting topics that are typically not covered in standard texts on the subject, incl. Dedekind’s duality, Tschirnhausen’s transformations and the lunes of Hippocrates.作者: 解脫 時間: 2025-3-25 14:23
Solving Algebraic Equations,ing roots applied to coefficients. We give examples of quantic equations for which such formulae exist (e.g. de Moivre’s quintics) and show that the ideas which work for equations of degrees up to 4 have no evident generalizations. We also briefly discuss “casus irreducibilis” related to cubic equations.作者: Commission 時間: 2025-3-25 17:26 作者: appall 時間: 2025-3-25 20:29
Supplementary Problems,e of the problems are suitably structured in order to introduce some interesting topics that are typically not covered in standard texts on the subject, incl. Dedekind’s duality, Tschirnhausen’s transformations and the lunes of Hippocrates.作者: Narcissist 時間: 2025-3-26 02:22 作者: Perigee 時間: 2025-3-26 08:13
Airline Organization in the 1980sand splitting fields of polynomials form exactly the same class. We further discuss a normal closure of a finite field extension. Galois extensions are those which are normal and separable. The separable extensions are discussed in the next chapter.作者: 評論者 時間: 2025-3-26 11:20 作者: 故意釣到白楊 時間: 2025-3-26 13:01 作者: 精致 時間: 2025-3-26 17:02 作者: 驚呼 時間: 2025-3-26 23:32
Airbreathing Hypersonic Propulsion show how to find similar formulae for cubic and quartic equations. We also explain why as early as the eighteenth century mathematicians started to doubt the possibility to find solutions for general quintic equations (or equations of higher degrees) using the four arithmetic operations and extract作者: Dri727 時間: 2025-3-27 02:04 作者: ALT 時間: 2025-3-27 05:35
https://doi.org/10.1007/978-3-662-02646-5 is a zero of a nontrivial polynomial with coefficients in K. We relate the elements of algebraic extensions to the corresponding polynomials and look at the structures of the simplest extensions .(.) of K. We also introduce the notion of the degree of a field extension and prove some of its propert作者: 畢業(yè)典禮 時間: 2025-3-27 13:17 作者: debouch 時間: 2025-3-27 15:08 作者: 熔巖 時間: 2025-3-27 18:39 作者: 人充滿活力 時間: 2025-3-28 01:58
https://doi.org/10.1007/978-3-658-33721-6d in most common situations). An extension of a field is separable if any irreducible polynomial with coefficients in this field does not have multiple zeros. All extensions of fields of characteristic zero and all finite extensions of finite fields have this property. For this reason, there are som作者: 強壯 時間: 2025-3-28 05:26
https://doi.org/10.1007/978-1-349-02425-4alois extensions, i.e. the extensions which are both normal and separable. One of the most central results is Galois’ correspondence between the subgroups of the Galois group of such an extension and the intermediate subfields of it. In the exercises, we find many examples and interesting properties作者: Functional 時間: 2025-3-28 08:25
https://doi.org/10.1057/9781403920096ed by the roots of 1. Even if such fields are simple to describe in purely algebraic terms, they are rich as mathematical objects. We explore some of their properties, which find different applications in number theory and algebra. Among many applications, there is a proof of a special case of Diric作者: pessimism 時間: 2025-3-28 10:36 作者: 代理人 時間: 2025-3-28 14:56 作者: IOTA 時間: 2025-3-28 19:23 作者: 合同 時間: 2025-3-29 02:22 作者: asthma 時間: 2025-3-29 03:41 作者: 故意 時間: 2025-3-29 10:34
Assessment and Clinical Patterns, or challenging problems covering various aspects of Galois theory. Several of these problems can be used as a starting point for student projects, such as problems related to the normal core of groups, Galois index, the notion of elements of field extensions essentially defined over a subfield. Som作者: transdermal 時間: 2025-3-29 11:31 作者: 責難 時間: 2025-3-29 16:50 作者: 繁忙 時間: 2025-3-29 20:58
https://doi.org/10.1007/978-3-662-02646-5 is a zero of a nontrivial polynomial with coefficients in K. We relate the elements of algebraic extensions to the corresponding polynomials and look at the structures of the simplest extensions .(.) of K. We also introduce the notion of the degree of a field extension and prove some of its properties such as the Tower Law.作者: lipids 時間: 2025-3-30 03:26 作者: 動物 時間: 2025-3-30 07:30 作者: 不能和解 時間: 2025-3-30 09:03 作者: hankering 時間: 2025-3-30 13:56 作者: Osmosis 時間: 2025-3-30 16:36
978-3-319-72325-9Springer International Publishing AG, part of Springer Nature 2018作者: 阻塞 時間: 2025-3-30 21:03 作者: engrave 時間: 2025-3-31 01:12 作者: reception 時間: 2025-3-31 05:55 作者: Generosity 時間: 2025-3-31 10:26
https://doi.org/10.1007/978-3-0348-7558-5This chapter contains the proofs to all theorems presented in the book. Only a few theorems, which are typically covered in an introductory course on groups, rings and fields are proved in the Appendix. A proof of the fundamental theorem of algebra is given in connection with the exercises in Chap. 13.作者: maladorit 時間: 2025-3-31 13:23
John E. Souness,Mark A. GiembyczThis chapter contains hints and answers to all exercises presented in Chaps. .–. where an answer can be expected.作者: 一瞥 時間: 2025-3-31 20:25
Polynomials and Irreducibility,In this chapter, we present facts on zeros of polynomials and discuss some basic methods to decide whether a polynomial is irreducible or reducible, including Gauss’ lemma, the reduction of polynomials modulo prime numbers ((irreducibility over finite fields), and Eisenstein’s criterion.作者: Freeze 時間: 2025-4-1 01:18
Proofs of the Theorems,This chapter contains the proofs to all theorems presented in the book. Only a few theorems, which are typically covered in an introductory course on groups, rings and fields are proved in the Appendix. A proof of the fundamental theorem of algebra is given in connection with the exercises in Chap. 13.作者: 豎琴 時間: 2025-4-1 01:57
Hints and Answers,This chapter contains hints and answers to all exercises presented in Chaps. .–. where an answer can be expected.作者: BUST 時間: 2025-4-1 10:04 作者: maintenance 時間: 2025-4-1 10:53
Solving Algebraic Equations, show how to find similar formulae for cubic and quartic equations. We also explain why as early as the eighteenth century mathematicians started to doubt the possibility to find solutions for general quintic equations (or equations of higher degrees) using the four arithmetic operations and extract
