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Graduate Texts in Mathematics #131
A First Course in Noncommutative Rings
Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.
- GenresMathematicsAlgebra
407 pages, Paperback
First published January 1, 1991
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Displaying 1 - 3 of 3 reviews
July 16, 2013
This is an awesome book for graduates and undergraduates who are fascinated by ring theory. I still use it all the time, and it was indispensable during my own graduate study.
The author has a very readable exposition style, and provides lots of clear examples and useful exercises. As a reader I really felt I was being taken on a purposeful stroll of ideas in ring theory.
In addition to "the staples" of noncommutative ring theory (the Artin-Wedderburn theorem and the Jacobson Density theorem) the book also goes into semiperfect and perfect rings and their cousins. This is the best introduction to such rings that I know of, since most other resources are basically at graduate level.
I saw one review complaining about terminology, but I will contradict the complaint wholeheartedly. The author's definitions and presentation are very clear and they are all completely within mainstream tolerance.
The author has a very readable exposition style, and provides lots of clear examples and useful exercises. As a reader I really felt I was being taken on a purposeful stroll of ideas in ring theory.
In addition to "the staples" of noncommutative ring theory (the Artin-Wedderburn theorem and the Jacobson Density theorem) the book also goes into semiperfect and perfect rings and their cousins. This is the best introduction to such rings that I know of, since most other resources are basically at graduate level.
I saw one review complaining about terminology, but I will contradict the complaint wholeheartedly. The author's definitions and presentation are very clear and they are all completely within mainstream tolerance.
July 20, 2010
The author doesn't define his terms, which makes the book a trial to read. I appreciate that reiterating basic definitions takes up space, but some terms are not used in the same way by everyone; in particular, definitions involving "right" and "left" are relative and likely to be variable.
Emblematic is the beginning of page 3: The author says "we have to differentiate carefully between left ideals and right ideals in R" -- and then fails to do so!
Also, the frequent usage of the phrase "quotienting out the ideal" sets my teeth on edge.
Emblematic is the beginning of page 3: The author says "we have to differentiate carefully between left ideals and right ideals in R" -- and then fails to do so!
Also, the frequent usage of the phrase "quotienting out the ideal" sets my teeth on edge.
February 12, 2012
The author doesn't define his terms, which makes the book a trial to read. I appreciate that reiterating basic definitions takes up space, but some terms are not used in the same way by everyone; in particular, definitions involving "right" and "left" are relative and likely to be variable.
Emblematic is the beginning of page 3: The author says "we have to differentiate carefully between left ideals and right ideals in R" -- and then fails to do so!
Also, the frequent usage of the phrase "quotienting out the ideal" sets my teeth on edge.
Emblematic is the beginning of page 3: The author says "we have to differentiate carefully between left ideals and right ideals in R" -- and then fails to do so!
Also, the frequent usage of the phrase "quotienting out the ideal" sets my teeth on edge.
Displaying 1 - 3 of 3 reviews