This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. The first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Grobner bases.The second part presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.
Les mer
This new edition, now in two parts, has been significantly reorganised and many sections have been rewritten. The first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. The second part presents many topics mentioned in the first part in greater depth and in more detail.
Les mer
Contents for Part 1: Course I: Classical formulasClassical number theoryCommutative ringsGroupsGalois theoryAppendix: Set theoryAppendix: Linear algebraCourse II: ModulesZorn's lemmaAdvanced linear algebraCategories of modulesMultilinear algebraCommutative algebra IIAppendix: Categorical limitsAppendix: Topological spacesBibliographySpecial notationIndexContents for Part 2: More groupsRepresentation theoryHomologyMore categoriesCommutative rings IIIBibliographyIndex.
Les mer

Produktdetaljer

ISBN
9781470441746
Publisert
2017-08-30
Utgiver
Vendor
American Mathematical Society
Høyde
229 mm
Bredde
152 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
1264

Biographical note

Joseph J. Rotman, University of Illinois at Urbana-Champaign, IL.