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A Course In Commutative Algebra

A Course In Commutative Algebra

This is a text for a basic course in commutative algebra, written in accordance with the following objectives. The course should be accessible to those who have studied algebra at the beginning graduate level. For general algebraic background, see my online text “Abstract Algebra: The Basic Graduate Year”, which can be downloaded from my web site www.math.uiuc.edu/∼ r-ash This text will be referred to as TBGY. The idea is to help the student reach an advanced level as quickly and efficiently as possible. In Chapter 1, the theory of primary decomposition is developed so as to apply to modules as well as ideals. In Chapter 2, integral extensions are treated in detail, including the lying over, going up and going down theorems. The proof of the going down theorem does not require advanced... Show More

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