This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interest ing context for the material covered. In addition, many results are reinterpreted from a geomet ric perspective, providing further insight and motivation for the study of commutative algebra. The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author’s sequel, Homological Methods in Commutative Algebra. Overall, this book is an excellent resource for advanced undergraduates and beginning gradu ate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valu able addition to any library.

Andrea Ferretti, graduated in medicine and surgery, specialized in orthopaedics and traumatology and in sports medicine and was fellow of Professor Lamberto Perugia and Professor Giancarlo Puddu. Since 2000 he is Full Professor and Chairman Of Orthopaedics at Sant’Andrea University Hospital in Rome and nowadays heir and representative of the prestigious School Of Knee Surgery founded by his masters. He was visiting professor in various universities around the world. Since 1990 he is team physician of the Italian national football team. He was as volleyball player and coach in the Italian National Volleyball League.

He is author of more than 350 published papers mainly in the field of knee surgery and sports medicine and author/coauthor of 3 books: one on volleyball injuries, one on sports traumatology and an orthopaedics and traumatology textbook.

As a researcher, his main topics of interest have always been the treatment of anterior cruciate ligamenttears and related instability with a special focus on the role of secondary restraints (anterolateral ligament, Segond fracture) on the rotational instability, as well as the effect of extra-articular reconstructions in controlling tibial rotation and pivot shift phenomenon.

He is member of the editorial board of Italian Journal of Orthopaedics and Traumatology (Springer) and reviewer of American Journal of Sports Medicine. He is invited as a speaker in all major orthopaedic international meetings, e.g. American Academy Of Orthopaedic Surgeons, American Orthopaedic Society For Sports Medicine, International Society Of Orthopaedics And Traumatology (SICOT), European Society Of Knee Surgery Sports Traumatology And Arthroscopy (ESSKA) etc.

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