Commutative Rings

Commutative Rings Synopsis

Commutative rings are a branch of abstract algebra that deals with the multiplication operation. This book examines the question, given any positive integer n, is there a commutative ring with identity that has n zero-divisions? This question is examined in stages through looking at local rings, reduced rings and finally commutative rings in general. In addition, several themes pertaining to the classification of minimal ring extensions are described. Some recent and new results on linear systems theory over commutative rings are also looked at. Finally, this book gives a brief history and summary of the active area of asymptotic stability of associated or attached prime ideals. Some of the old and new results about the asymptotic properties of associated and attached prime ideals related to injective, projective or flat modules, are discussed.

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