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Ring Theory (Student Edition) by Louis H. Rowen
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Ring Theory (Student Edition) written by Louis H. Rowen
This volume is an abridged edition of Ring Theory, volumes 1 and 2, designed to be more palatable (and affordable) to students. The original two volumes aimed to serve the dual purpose of research guides and texts, and so a layered approach was adopted, consisting of text, supplements, appendices, exercises, and digressions.
Since my original manuscript had already been pared down as far as I could bear before publication, I did not cherish the task of deleting any other topics. However, a fair amount of material in the two volumes is aimed at those intending to specialize in ring theory, and might not be missed in a general ring theory course. Another side benefit of this project is the opportunity to correct a few gross mistakes in the two volume edition. I thank those people who took the time to send in lists of misprints and more serious mistakes.
In line with the relatively modest goals of a graduate text, the more technical exercises and digressions pointing to further research have been deleted; proofs of introductory results, which may be fresh in the mind of a graduate student (and available in standard texts such as Jacobson's Basic Algebra I), have also been removed. In the later chapters, material often has been cut if it was not essential for proving the principal theorems. Nevertheless, the format and numbering of results matches the original two volumes, enabling the reader to consult them for further edification. Heavy deletions were made from Chapter 7 (division algebras). Nevertheless, virtually all the basic structural results in it can be obtained through elementary means; these techniques sometimes were lost in the original version of the chapter as the theory became increasingly complicated. The necessities of space gave me an excuse to build the theory of simple algebras directly from cyclic algebras; in retrospect, and in view of the Merkurjev-Suslin theorem, one might argue that this is the "right" way to develop the subject. Similarly, I took the opportunity to replace the proof of Shirshov's theorem in §6.3 with Belov's new proof, which is easier and more direct.
(Louis H. Rowen)
Book Detail :-
Title: Ring Theory
Edition: Student Edition
Author(s): Louis H. Rowen
Publisher: Academic Press
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About Author :-
Author Louis H. Rowen Professor at Department of Mathematics, Bar-Ilan University, Tel Aviv District, Israel.
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Book Contents :-
Ring Theory (Student Edition) written by Louis H. Rowen cover the following topics.
0. General Fundamentals
1. Construction of Rings
2. Basic Structure Theory
3. Rings of Fractions and Embedding Theorems
4. Categorical Aspects of Module Theory
5. Homology and Cohomology
6. Rings with Polynomial Identities and Affine Algebras
7. Central Simple Algebras
8. Rings from Representation Theory
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