basic abstract algebra ebook
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: basic abstract algebra ebook
basic abstract algebra ebook
Basic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook gebra: The Basic Graduate YearRobert B. AshPREFACEThis is a text for the basic graduate sequence in abstract algebra, offered by most universities. We study fundamental algebraic structures, namely groups, rings, fields and modules, and maps between these structures. The techniques are used in many basic abstract algebra ebook areas of mathematics, and there are applications to physics, engineering and computer science as well. In addition, I have attempted to communicate thbasic abstract algebra ebook
e intrinsic beauty of the subject. Ideally, the reasoning underlying each step of a proof should be completely clear, but the overall argument should Basic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook resolve the conflict.My primary goal is to help the rentier learn the subject, and there are times when informal or intuitive reasoning leads to greater understanding than a formal proof. In the text, there are three types of informal arguments:1The concrete or numerical example with all features of basic abstract algebra ebook the general case. Here, the example indicates how the proof should go, ami the formalization amounts to substituting Greek let ters for numbers. Therbasic abstract algebra ebook
e is no essential loss of rigor in the informal version.2Brief informal surveys of huge areas. There are two of these. p-adic numbers ami group represBasic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook hich do not reveal why a result is true. In this case, explicit references to a precise formalization are given. 1 am not saying that the formal proof should be avoided, just that the basic graduate year, where there are many pressing matters to cope with, may not be the appropriate place, especiall basic abstract algebra ebook y when the result rather than the proof technique is used in applications.1 would estimate that alwnt 90 percent of the text is written in conventionabasic abstract algebra ebook
l style, and I hope that the book will be used as a classroom text as well as a supplementary reference.Solutions to al) problems arc included in the Basic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook this allows for wider coverage as well as reinforcement of the basic ideas.Chapters 1-4 cover basic properties of gronjxi, rings, fields ami modules. The typical student will have seen some but not all of this material in an undergraduate algebra course. [It should be possible to base an undergradu basic abstract algebra ebook ate course on Chapters 1-4, traversed at a suitable pace with detailed coverage of the exercises.] In Chapter 1. the fundamental structure theorems fobasic abstract algebra ebook
r finitely generated modules over a principal ideal domain arc developed concretely with the aid of the Smith normal form. Students will undoubtedly bBasic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook on sets leads to a nice application to combinatorics as well as the fundamental Sylow theorems and some results on simple groups. Analysis of normal ami subnormal series leads to the .Ionian-Holder theorem and to solvable and nilpotent groups. The final section, on defining a group by generators am basic abstract algebra ebook i relations, concentrates on practical cases where the structure of a group can be deduced from its presentation. Simplicity of the alternating groupsbasic abstract algebra ebook
and semidirect products arc covered in the exercises.Chapter 6 goes quickly to the fundamental theorem of Galois theory; this is possible because theBasic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook Galois group, we proceed to finite fields, which are of great importance in applications, and cyclotomic fields, which arc fundamental in algebraic number theory. The Galois group of a cubic is treated in detail, ami the quartic is covered in an appendix. Sections on cyclic and Kummer extensions are basic abstract algebra ebook followed by Galois’ fundamental theorem on solvability by radicals. The last section of the chapter deals with transcendental extensions ami transcenbasic abstract algebra ebook
dence bases.In the remaining chapters, we begin to apply the results and methoils of abstract algebra to related areas. The title of each chapter begiBasic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook including categories and functors).Algebraic number theory and algebraic geometry are the two major areas that use the tools of commutative algebra (the theory of commutative rings). In Chapter 7, after an example showing how algebra can be applied in number theory, we assemble some algebraic equipm basic abstract algebra ebook ent: integral extensions, norms, traces, discriminants, Noethcrian ami Artinian modules and rings. We then prove the fundamental theorem on unique facbasic abstract algebra ebook
torization of ideals in a Dedekind domain. The chapter concludes with an informal introduction to p-adic numbers and some ideas from valuation theory.Basic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook nnllstellensatz. Several equivalent versions of the nullstellensatz arc given, as well as some corollaries wit h geometric significance. Further geometric considerations lead to the useful algebraic techniques of localization and primary decomposition. The remainder of the chapter is concerned with basic abstract algebra ebook the tensor product and its baric properties.Chapter 9 Iregins the study of noncommutative rings and their modules. The Ixasic theory of simple and sembasic abstract algebra ebook
isimple rings and modules, along with Schur’s lemma ami Jacobson's theorem, combine to yield Wedderburn’s theorem on the structure of scmisimple ringsBasic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook resentations. Maschke’s theorem on semisimplicity of modules over the group algebra Is proved. The introduction of the Jacobson radical gives more insight into the structure of rings and modules. The chapter ends with the I lopkins-Levitzki theorem that an Artinian ring is Noetherian, and the useful basic abstract algebra ebook lemma of Nakayama,In Chapter 10, we introduce some of the tools of homological algebra. Wailing until the last chapter for this is a deliberate decisbasic abstract algebra ebook
ion. Students need as much exposure as possible to specific algebraic systems before they can appreciate the broad viewpoint of category theory. Even Basic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook the reader, functors arc introduced via the familiar examples of horn and tensor. No attempt is made to work with general abelian categories. Instead, we stay within the category of modules and study projective, injective ami flat modules.In a supplement, we go much farther into homological algebra basic abstract algebra ebook than is usual in the liasic algebra sequence. We do this to help students cope with the massive formal machinery that makes it so difficult to gain abasic abstract algebra ebook
working knowledge of this area. We concentrate on the results that arc most useful in applications: the long exact homology sequence and the propertiBasic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract Alg basic abstract algebra ebook ormal proof is entirely appropriate, because doing so will help improve algebraic skills. The point is not to avoid difficulties, but to make most efficient use of the finite amount of time available.Robert IỈ. AshOctol >er 2090 basic abstract algebra ebook Basic Abstract Algebra For Graduate Students and Advanced Undergraduates ^UỂSểEì^..4'■V ũíì&>—Aee ht IíRobert B. Ashpage 1 of lừuiitniAtUưAbstract AlgGọi ngay
Chat zalo
Facebook