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.
John Lee was born and raised a few miles north of London in the pub-strewn city of St. Albans before heading to university (okay, polytechnic) in Leicester. Eager for overseas adventure, he next finagled his way into western Canada's University of Victoria to study politics before teaching English in Tokyo and then taking a life-changing trek on the Trans-Siberian Railway. By the time the train trundled into Moscow, he had decided to abandon all reason and become a full-time freelance travel writer. More than 10 years later, he's still doing it. An adopted Vancouverite for most of that time, John's travel writing has appeared in more than 125 major newspapers and magazines around the world and his trips have taken him from New Zealand's Fox Glacier to the pubs of Galway and the barbecue pits of Texas. Since 2004, he's also been a Lonely Planet guidebook author and has written 15 books for the company. For more on what he's up to, visit