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 ...
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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 Grobner 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. (GSM/114)
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Add this copy of Advanced Modern Algebra to cart. $48.27, very good condition, Sold by quasifibration rated 4.0 out of 5 stars, ships from Toronto, ON, CANADA, published 2002 by Prentice Hall.
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Very Good. pp. 1040. ORIGINAL FIRST HARDCOVER EDITION; second (revised) printing (edition); has some shelf wear; otherwise a tight bright unmarked copy in very good shape overall; appears unread!
Add this copy of Advanced Modern Algebra to cart. $58.31, new condition, Sold by quasifibration rated 4.0 out of 5 stars, ships from Toronto, ON, CANADA, published by American Mathematical Society.
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New. American Mathematical Society, 2016. New. American Mathematical Society, 2016. Hard cover. 6. No dust jacket. Contains: Illustrations. Audience: General/trade. BRAND NEW hardcover; third edition; all pages are printed and bound in red buckram in a lay flat binding; both parts (volumes) are bound as one; a tight bright unmarked copy; book lays open flat with ease; never read!
Add this copy of Advanced Modern Algebra to cart. $77.00, good condition, Sold by Moe's Books rated 4.0 out of 5 stars, ships from Berkeley, CA, UNITED STATES, published 2002 by Pearson Educations, Inc.
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Good. No jacket. Out of print. Spine is shaken but secure. Cover is worn, especially along edges. Back cover has pen mark over bar code. Text block is tanned, but legibility is not affected. Inside front cover has previous owner's signature. Pages are unmarked.
Add this copy of Advanced Modern Algebra to cart. $79.69, new condition, Sold by quasifibration rated 4.0 out of 5 stars, ships from Toronto, ON, CANADA, published by Prentice Hall.
Add this copy of Advanced Modern Algebra to cart. $79.84, new condition, Sold by quasifibration rated 4.0 out of 5 stars, ships from Toronto, ON, CANADA, published by American Mathematical Society.
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New. Providence: American Mathematical Society, 2010. 2nd Revised edition. Revised. New. Providence: American Mathematical Society, 2010. 2nd Revised edition. Revised. Hard cover. 6. null 1008 p. Graduate Studies in Mathematics. Audience: Adult education. BRAND NEW hardcover; SECOND edition; all pages are printed and bound in a light blue (hardcover) buckram in a lay flat binding; a tight bright unmarked copy; book lays open flat with ease; never read! .
Add this copy of Advanced Modern Algebra: Third Edition, Part 1 to cart. $102.00, very good condition, Sold by Maxwell's House of Books rated 3.0 out of 5 stars, ships from La Mesa, CA, UNITED STATES, published 2015 by American Mathematical Society.
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Fine. Providence: American Mathematical Society, edition. Revised. Fine. Providence: American Mathematical Society, 2010. 2nd Revised edition. Revised. Hard cover. 5. Fine. No dust jacket. 1008 p. Graduate Studies in Mathematics. ORIGINAL HARDCOVER; SECOND edition; has very minor shelf wear; otherwise a tight bright unmarked copy in excellent shape overall; appears unread!
Add this copy of Advanced Modern Algebra to cart. $125.59, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2002 by Pearson College Div.
Add this copy of Advanced Modern Algebra (Graduate Studies in to cart. $126.90, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2010 by Amer Mathematical Society.
I am a retired professor of mathematics from a major university. My field of rsearch was algebra. Previous books by Rotman were very attractive and so I was curious about this 1012 page algebra tome. The reason one writes a book is that at some point one thinks one has organized the material in one's mind successfully and putting the ideas down on paper clarifiys or validates this belief. So Rotman apparantly has reached this point in his thoughts about general algebra. I don't think he has anything to offer us that makes this book a needed addition to the literature. First of all the book is too long. It must have taken Rotman years to write this book and we don't have years to absorb all of it. Due to the continual mathematical "flashbacks" I don't think the book is very useful as a general reference. Here's what I recommend: Jacobson's two volumes Basic Algebra I and II have been reprinted inexpensively by Dover at under US$20 each. Volume I can actually be read and is enough algebra background for anyone entering research. Volume II is an excellent reference and supplies more than enough background for a professioal. However I must credit Rotman with very clear explanations of the material and proofs. I just wish this book was up to the level of Rotman's excellent group theory and homological algebra books.
