Advanced modern algebra / (Record no. 823)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 03063cam a2200325 a 4500 |
| 001 - CONTROL NUMBER | |
| control field | 16020657 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20230114171232.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 091212s2010 riua b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780821847411 (alk. paper) |
| ISBN | 9781470419165 |
| ISBN | 0821847414 (alk. paper) |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512 |
| Book number | ROT/A |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Rotman, Joseph J., |
| 245 10 - TITLE STATEMENT | |
| Title | Advanced modern algebra / |
| Statement of responsibility, etc | Joseph J. Rotman. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2nd ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Providence, R.I. : |
| Name of publisher | American Mathematical Society, |
| Year of publication | c2010. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | xvi, 1008 p. : |
| Other physical details(ill.) | ill. ; |
| Dimensions(size) | 27 cm. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Graduate studies in mathematics ; |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Groups I -- Commutative rings I -- Galois theory -- Groups II -- Commutative rings II -- Rings -- Representative theory -- Advanced linear algebra -- Homology -- Commutative rings III. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | "This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen-Schreier theorem (subgroups of free groups are free). The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Gröbner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn-Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra. Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic K-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization."--Publisher's description. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Algebra. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | Gratis Book |
| Koha issues (borrowed), all copies | 7 |
| Withdrawn status | Lost status | Damaged status | Not for loan | Collection code | Home library | Current library | Date acquired | Full call number | Accession Number | Price effective from | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Not withdrawn | Not Lost | not damaged | Central Library, IIT Bhubaneswar | Central Library, IIT Bhubaneswar | 21/11/2015 | 512 ROT/A | GB475 | 21/11/2015 | Gratis Book |