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Commutative Rings (Lectures in Mathematics)
Posted on 2010-04-10
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More Irving Kaplansky " From the preface "Edited" My intention is to give an account of some topics in the theory of commutative rings in a way that is accessible to a reader with a modest background in modern algebra; I assume only an acquaintance with the definitions and most elementary properties of rings, ideals, and modules. More exactly, this is true till chapter "4-1 Homology", here I presuppose the theory of homological dimension as developed on "KAPLANSKY, Fields and Rings", and chapter "4-4 Change of Rings for Injective Dimension" where use of the long exact sequence for Ext begins. I hope that readers will find it feasible to go on from this book to a deeper study of the literature. It would be most urgent to learn the theory of completion and the Cohen structure theorems. I have inserted numerous exercises, partly to cover additional material of lesser importance, and partly to give the reader a chance to test his growing skill. There is occasional reliance on the exercises as part of the exposition, and I hope no reader will find this inconvenient. or or "
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