Lectures on Modules and Rings [electronic resource] /
Textbook writing must be one of the cruelest of self-inflicted tortures. - Carl Faith Math Reviews 54: 5281 So why didn't I heed the warning of a wise colleague, especially one who is a great expert in the subject of modules and rings? The answer is simple: I did not learn about it until it was too late! My writing project in ring theory started in 1983 after I taught a year-long course in the subject at Berkeley. My original plan was to write up my lectures and publish them as a graduate text in a couple of years. My hopes of carrying out this plan on schedule were, however, quickly dashed as I began to realize how much material was at hand and how little time I had at my disposal. As the years went by, I added further material to my notes, and used them to teach different versions of the course. Eventually, I came to the realization that writing a single volume would not fully accomplish my original goal of giving a comprehensive treatment of basic ring theory. At the suggestion of Ulrike Schmickler-Hirzebruch, then Mathematics Editor of Springer-Verlag, I completed the first part of my project and published the write up in 1991 as A First Course in Noncommutative Rings, GTM 131, hereafter referred to as First Course (or simply FC).
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Format: | Texto biblioteca |
Language: | eng |
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New York, NY : Springer New York : Imprint: Springer,
1999
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Subjects: | Mathematics., Algebra., |
Online Access: | http://dx.doi.org/10.1007/978-1-4612-0525-8 |
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KOHA-OAI-TEST:2120722018-07-30T23:45:23ZLectures on Modules and Rings [electronic resource] / Lam, T. Y. author. SpringerLink (Online service) textNew York, NY : Springer New York : Imprint: Springer,1999.engTextbook writing must be one of the cruelest of self-inflicted tortures. - Carl Faith Math Reviews 54: 5281 So why didn't I heed the warning of a wise colleague, especially one who is a great expert in the subject of modules and rings? The answer is simple: I did not learn about it until it was too late! My writing project in ring theory started in 1983 after I taught a year-long course in the subject at Berkeley. My original plan was to write up my lectures and publish them as a graduate text in a couple of years. My hopes of carrying out this plan on schedule were, however, quickly dashed as I began to realize how much material was at hand and how little time I had at my disposal. As the years went by, I added further material to my notes, and used them to teach different versions of the course. Eventually, I came to the realization that writing a single volume would not fully accomplish my original goal of giving a comprehensive treatment of basic ring theory. At the suggestion of Ulrike Schmickler-Hirzebruch, then Mathematics Editor of Springer-Verlag, I completed the first part of my project and published the write up in 1991 as A First Course in Noncommutative Rings, GTM 131, hereafter referred to as First Course (or simply FC).1 Free Modules, Projective, and Injective Modules -- 1. Free Modules -- 2. Projective Modules -- 3. Injective Modules -- 31. Matlis’ Theory -- 2 Flat Modules and Homological Dimensions -- 4. Flat and Faithfully Flat Modules -- 41. Faithfully Flat Modules -- 5. Homological Dimensions -- 3 More Theory of Modules -- 6. Uniform Dimensions, Complements, and CS Modules -- 7. Singular Submodules and Nonsingular Rings -- 8. Dense Submodules and Rational Hulls -- 4 Rings of Quotients -- 9. Noncommutative Localization -- 10. Classical Rings of Quotients -- 11. Right Goldie Rings and Goldie’s Theorems -- 12. Artinian Rings of Quotients -- 5 More Rings of Quotients -- 13. Maximal Rings of Quotients -- 14. Martindale Rings of Quotients -- 6 Frobenius and Quasi-Frobenius Rings -- 15. Quasi-Frobenius Rings -- 16. Frobenius Rings and Symmetric Algebras -- 7 Matrix Rings, Categories of Modules, and Morita Theory -- 17. Matrix Rings -- 18. Morita Theory of Category Equivalences -- 19. Morita Duality Theory -- References -- Name Index.Textbook writing must be one of the cruelest of self-inflicted tortures. - Carl Faith Math Reviews 54: 5281 So why didn't I heed the warning of a wise colleague, especially one who is a great expert in the subject of modules and rings? The answer is simple: I did not learn about it until it was too late! My writing project in ring theory started in 1983 after I taught a year-long course in the subject at Berkeley. My original plan was to write up my lectures and publish them as a graduate text in a couple of years. My hopes of carrying out this plan on schedule were, however, quickly dashed as I began to realize how much material was at hand and how little time I had at my disposal. As the years went by, I added further material to my notes, and used them to teach different versions of the course. Eventually, I came to the realization that writing a single volume would not fully accomplish my original goal of giving a comprehensive treatment of basic ring theory. At the suggestion of Ulrike Schmickler-Hirzebruch, then Mathematics Editor of Springer-Verlag, I completed the first part of my project and published the write up in 1991 as A First Course in Noncommutative Rings, GTM 131, hereafter referred to as First Course (or simply FC).Mathematics.Algebra.Mathematics.Algebra.Springer eBookshttp://dx.doi.org/10.1007/978-1-4612-0525-8URN:ISBN:9781461205258 |
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Mathematics. Algebra. Mathematics. Algebra. Mathematics. Algebra. Mathematics. Algebra. Lam, T. Y. author. SpringerLink (Online service) Lectures on Modules and Rings [electronic resource] / |
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Textbook writing must be one of the cruelest of self-inflicted tortures. - Carl Faith Math Reviews 54: 5281 So why didn't I heed the warning of a wise colleague, especially one who is a great expert in the subject of modules and rings? The answer is simple: I did not learn about it until it was too late! My writing project in ring theory started in 1983 after I taught a year-long course in the subject at Berkeley. My original plan was to write up my lectures and publish them as a graduate text in a couple of years. My hopes of carrying out this plan on schedule were, however, quickly dashed as I began to realize how much material was at hand and how little time I had at my disposal. As the years went by, I added further material to my notes, and used them to teach different versions of the course. Eventually, I came to the realization that writing a single volume would not fully accomplish my original goal of giving a comprehensive treatment of basic ring theory. At the suggestion of Ulrike Schmickler-Hirzebruch, then Mathematics Editor of Springer-Verlag, I completed the first part of my project and published the write up in 1991 as A First Course in Noncommutative Rings, GTM 131, hereafter referred to as First Course (or simply FC). |
format |
Texto |
topic_facet |
Mathematics. Algebra. Mathematics. Algebra. |
author |
Lam, T. Y. author. SpringerLink (Online service) |
author_facet |
Lam, T. Y. author. SpringerLink (Online service) |
author_sort |
Lam, T. Y. author. |
title |
Lectures on Modules and Rings [electronic resource] / |
title_short |
Lectures on Modules and Rings [electronic resource] / |
title_full |
Lectures on Modules and Rings [electronic resource] / |
title_fullStr |
Lectures on Modules and Rings [electronic resource] / |
title_full_unstemmed |
Lectures on Modules and Rings [electronic resource] / |
title_sort |
lectures on modules and rings [electronic resource] / |
publisher |
New York, NY : Springer New York : Imprint: Springer, |
publishDate |
1999 |
url |
http://dx.doi.org/10.1007/978-1-4612-0525-8 |
work_keys_str_mv |
AT lamtyauthor lecturesonmodulesandringselectronicresource AT springerlinkonlineservice lecturesonmodulesandringselectronicresource |
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