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Customer Reviews (15)

Elegant but terse
This book is written extremely well.It is very elegantly worded, to the point where it is very difficult to follow.A glossary would have been nice. I found myself backtracking several times per section to keep track of the jargon flying around.I recommend Stillwell's undergraduate and Robert Ash's graduate books instead.Ash's book is less elegant than this, but more straightforward and formatted more accessibly.Also, the title may be one of the biggest misnomers in the history of textbooks; "Basic Algebra I" sounds like the title of a junior high textbook, not a graduate school-level one.I'm guessing that this is a good reference if you already know abstract algebra like the back of your hand; but to learn it, there are many more accessible texts at this level.

The man is great, the book is not
This is not an easy book to learn from.The material is there but organized in a very poor way.Important results and theorems are often hidden in the middle of page long paragraphs.The index is so bad they might as well not have included it.The information is all there, but unless you read every word in the text from beginning to end, you just won't be able to get to it.I used Hungerford to get through my first graduate classes in algebra, which is too brief but definitely a step up from this.This is a poorly organized text written by a truly great mathematician.

the best intro to algebra for future mathematicians
This book is by an expert algebraist who has rewritten his earlier introduction to algebra from the experience gained after 20 years as a Yale professor. It contains correct insightful proofs, carefully explained as clearly as possible without compromising their goal of reaching the bottom of each topic.

Other books say that one cannot square the circle with ruler and compass because it would require solving an algebraic equation with rational coefficients whose root is pi, and after all pi is a transcendental number. But Jacobson also proves that pi is a transcendental number, so as not to leave a logical gap. Naturally the burden on the student is somewhat higher than if he is merely told this fact without proof.

It is true that some other books include many more examples, and discuss them at extreme length, whereas Jacobson's book is less than 500 pages, hence cannot include as many words.But Jacobson's words are sometimes far better chosen, as he clearly understands the material at greater depth than other authors.

In his introduction to R modules, he discusses the most natural possible ring that acts on an abelian group: the ring of its endomorphisms.This is the true motivation behind the usefulness of R modules structures but is not even hinted at in most other books.

In his treatment of factorization in Noetherian domains, Jacobson carefully proves the existence of a single irredudible factor before proving existence of a complete factorization, thus avoiding perfectly a logical trap that some authors do not even notice.

In his discussion of the structure theory of finitely generated modules over a pid, he gives the concrete proof using diagonalization of matrices, that will actually be applied later to linear transformations, rather than some abstract existence proof that will be useless later, as many other authors do.

This sort of careful attention to the internal structure of the subject, and expert skill at presenting it correctly and clearly, are possible only to someone like Jacobson who is a true master of his area.I have only recently, as a mature mathematician, become aware of how wonderful his book really is for beginners who want to learn the subject correctly, from the beginning.

Some students not used to reading paragraphs, have been frustrated at his style of presentation, without realizing the superiority of his content.I can only recommend that those readers try harder to read his book, as it will repay far more than other sources.

Jacobson has made a sincere, and I think very successful effort, to write his 2 volumes on 2 different levels of sophistication, the first being back - bendingly clear and painstakingly organized as to the true logic of the subject.

After choosing a different source for my beginning graduate algebra course, I discovered the superiority of Jacobson, and wondered in amazement how such a great work could have been allowed to go out of print. After reading these reviews I understand. The readers who criticize the experts have eventually managed to veto the use of their works in classes. This makes the market share fall, and the books cease to exist. We have been obliged recently to remove Jacobson from our list of PhD references, in spite of its excellence, because it is out of print. This is a real disservice to our PhD students seeking to understand the material they will need to use.

Average students, i.e. most of us, have the right to learn a subject, but we should not have the right, and we are unwise to try, to vote the best books out of existence simply because we cannot understand them.Let us aspire to understanding the deeper treatment in Jacobson's book.Let's put our copy of Jacobson away and save it, if we cannot yet read it.

Clearly it is not the first book for everyone, but it is still perhaps the best, treatment of the material in existence to my knowledge at the upper undergraduate - graduate level, for the student who aspires to real mastery and understanding.If you want to be mathematician, you should get and read this book above others.Indeed the AMA rates both volumes of Jacobson as "essential" for every undergraduate library.

good textbook. but....
During the lecture on the abstract algebra 1, Jacobson's book was the main textbook. Although his book is regarded as "bible" by some professors, I cannot help confessing thath i need another reference book which explains the material in more detail and more carefully. So I consult Frayleigh's algebra textbook whenever I hit upon something difficult to understand on jacobson's. Frayleigh's book is kinder, not to economize explanationsand examples. Jacobson is one of the top-class mathematian, but his fame doesn't assure his book's efficiency. His book is written too abstractively. I don't want to recommend this book to the beginers although it has the title "basic".

Excellent!
I'm truly shocked that this book has received such low reviews.This is not an easy book, but it shouldn't be faulted for that.It's clear and beautifully written, and it's been a pleasure to work through.Additionally, the chapters are divided into sections that are 'bite size' with exercises at the end of each, which has made it well suited for regular daily study.I would highly recommend it to any student with some mathematical maturity who wishes to get a good foundation in the subject. ... Read more

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Not so basic; very wordy
This is the second part of a classic (I suspect it's a "classic" in the sense of the word used by physics majors describing Jackson's E&M book) textbook series in abstract algebra, originally intended for undergraduates, but closer to the graduate level.The title is a misnomer, as this is one of the most advanced algebra books I've ever read.This volume starts with category theory and continues from there.

The writing is very elegant, like its companion volume, to the point where it slows down the reader considerably.Like the first volume, there is no glossary.This volume is much more advanced than the first volume; while I could see undergrad seniors using volume one in a year-long 500-level undergrad/grad course, this volume is closer to a 600 or even 700 level.The main challenge is picking out all of the concepts from the script, and hanging on to them long enough to make it through the next chapter.

Some things I would have loved to see:
More examples.
A glossary of definitions.
A table of theorems and lemmas.
A more direct approach.
A table comparing the various structures and the types of morphisms by each structure. Wikipedia has a nice table of structures, but I have yet to see a table with, for example, a row labeled "Isomorphism", with columns for monoids, groups, rings, fields, modules, and categories, and values showing the main differences in concepts.Such tables convey a lot of information quickly.

Not so very basic
I bought both the Basic Algebra I and II in order to help my grandson review algebra before trying to go to college. Both of these books are far advanced for a basic math course. They are totally unsuited for my purposes. They read like one of those government technical seminars where everyone falls asleep. This book is only useful if you are already a math nerd.

Not that basic
It is indeed not an undergraduate level book, but Jaconson I&II
form a great overall introduction to algebra for the budding
algebraist. We used Jacobson I as the intro algebra text for
graduate students at Berkeley, and it can be recommended for
first or second year students (and beyond.) It forms a part of]
the trilogy of "Don't Let the Name Fool You" of not that basic
mathematics book with Weil's Basic Number Theory and Serre's
A Course in Arithmetic.

Excellent
Basic Algebra II is much better organized than Basic Algebra I, and it is an outstanding reference for the algebra that every Ph.D. graduate student should know.Perhaps the decision to prove Wedderburn's theorem via Morita theory was unfortunate since it makes the former seem more inaccessible than it really is, but otherwise I cannot fault the exposition. One word of warning: if your main interest is algebraic number theory, then Lang's _Algebra_ is probably a better reference since Jacobson omits several topics that are crucial for the number theorist.

Not really for undergraduates
The claim by Book News that this is a book addressed to undergraduates is just plain wrong.In fact, this book is even difficult for the average graduate student.The title `Basic Algebra' might be at the root of this misundestanding. This is a classic book and a standard reference for abstract algebra at a relatively advanced level. ... Read more

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Definitive treatment covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, and more. Classic handbook for researchers and students; useable in graduate courses or for self-study.
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A Gem from The Past
I recently noticed that my early edition of this book could not be found, so, I ordered another copy. It is just as good as my recollections some fourty and more years later told me. There is really no more to be said, despite more recent work, and the discoveries by physicists between 1965 and 1995. I think we all hope that Lie Algebras will be just as useful in interpretation of results soon to be forthcoming from the European Super Collider, and we hope from an even bigger paticle accelerator built somewhere in the United States. ... Read more

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The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation. ... Read more

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Finite-Dimensional Division Algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the so-called "multiplication algebras of Riemann matrices". The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution;their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm.

Corrections of the 1^st edition (1996) carried out on behalf of N. Jacobson (deceased) by Prof. P.M. Cohn (UC London, UK).

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Kapitel: Emmy Noether, Joachim Seyppel, René Girard, James Mckeen Cattell, Olga Taussky-Todd, Nathan Jacobson, Machteld Mellink, Erich Frank, Felix Gilbert, Lily Ross Taylor, Valentin Müller, David Widder, Helen Taft. Aus Wikipedia. Nicht dargestellt. Auszug: Amalie Emmy Noether, German pronunciation: , (23 March 1882 - 14 April 1935) was a German-born mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of rings, fields, and algebras. In physics, Noether's theorem explains the fundamental connection between symmetry and conservation laws. She was born to a Jewish family in the Bavarian town of Erlangen; her father was the mathematician Max Noether. Emmy originally planned to teach French and English after passing the required examinations, but instead studied mathematics at the University of Erlangen, where her father lectured. After completing her dissertation in 1907 under the supervision of Paul Gordan, she worked at the Mathematical Institute of Erlangen without pay for seven years. In 1915 she was invited by David Hilbert and Felix Klein to join the mathematics department at the University of Göttingen, a world-renowned center of mathematical research. The philosophical faculty objected, however, and she spent four years lecturing under Hilbert's name. Her habilitation was approved in 1919, allowing her to obtain the rank of privatdozent. Noether remained a leading member of the Göttingen mathematics department until 1933; her students were sometimes called the "Noether boys". In 1924, Dutch mathematician B. L. van der Waerden joined her circle and soon became the leading expositor of Noether's ideas: her work was the foundation for the second volume of his influential 1931 textbook, Moderne Algebra. By the time of her plenary ad...http://booksllc.net/?l=de ... Read more