An Elementary Approach to Homological Algebra: Monographs and Surveys in Pure and Applied Mathematics
Autor L. R. Vermanien Limba Engleză Hardback – 28 mai 2003
An Elementary Approach to Homological Algebra fills that void. Designed to meet the needs of beginning graduate students, it presents the material in a clear, easy-to-understand manner. Complete, detailed proofs make the material easy to follow, numerous worked examples help readers understand the concepts, and an abundance of exercises test and solidify their understanding.
Often perceived as dry and abstract, homological algebra nonetheless has important applications in many important areas. The author highlights some of these, particularly several related to group theoretic problems, in the concluding chapter. Beyond making classical homological algebra accessible to students, the author's level of detail, while not exhaustive, also makes the book useful for self-study and as a reference for researchers.
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Specificații
ISBN-13: 9781584884002
ISBN-10: 1584884002
Pagini: 326
Ilustrații: 1000 equations
Dimensiuni: 156 x 234 x 24 mm
Greutate: 0.6 kg
Ediția:1
Editura: CRC Press
Colecția CRC Press
Seria Monographs and Surveys in Pure and Applied Mathematics
ISBN-10: 1584884002
Pagini: 326
Ilustrații: 1000 equations
Dimensiuni: 156 x 234 x 24 mm
Greutate: 0.6 kg
Ediția:1
Editura: CRC Press
Colecția CRC Press
Seria Monographs and Surveys in Pure and Applied Mathematics
Public țintă
ProfessionalCuprins
Modules. Categories and Functors. Projective and Injective Modules. Homology of Complexes. Derived Functors. Torsion and Extension Functors. The Functor Ext. Hereditary and Semi-Hereditary Rings. Universal Coefficient Theorem. Dimensions of Modules and Rings. Cohomology of Groups.
Recenzii
"The book is a self-contained one and there are … complete proofs for all the results. In our opinion, it is a highly recommended introductory book in Homological Algebra for everyone interested in this subject."
- Zentralblatt MATH, 1045
"… [T]he author on the one hand has included the underlying basics, model and category theory, which are developed from scratch. On the other hand the elementary notions and results of homological algebra are treated in great detail and often their importance within that theory as well as in applications is shown. … All in all the author has managed … admirably to reach the goal he has set [for] himself."
- Monatshefte fur Mathematik
"When I next teach an introductory course on homological algebra at my institution, I will certainly consider adopting this book as the textbook for the course.
-Mathematical Reviews
- Zentralblatt MATH, 1045
"… [T]he author on the one hand has included the underlying basics, model and category theory, which are developed from scratch. On the other hand the elementary notions and results of homological algebra are treated in great detail and often their importance within that theory as well as in applications is shown. … All in all the author has managed … admirably to reach the goal he has set [for] himself."
- Monatshefte fur Mathematik
"When I next teach an introductory course on homological algebra at my institution, I will certainly consider adopting this book as the textbook for the course.
-Mathematical Reviews
Descriere
Often perceived as dry and abstract, homological algebra nonetheless has important applications in a number of important areas, including ring theory, group theory, representation theory, and algebraic topology and geometry. Although the area of study developed almost 50 years ago, a textbook at this level has never before been available. An Elementary Approach to Homological Algebra fills that void. Designed to meet the needs of beginning graduate students, the author presents the material in a clear, easy-to-understand manner with many examples and exercises. The book's level of detail, while not exhaustive, also makes it useful for self-study and as a reference for researchers.