{"product_id":"free-ideal-rings-and-localization-in-general-rings-book-p-m-cohn-9780521853378","title":"Free Ideal Rings and Localization in General Rings","description":"Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49762728870161,"sku":"GOR013778897","price":28.5,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51003269710097,"sku":"NIN9780521853378","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52481890418961,"sku":"NLS9780521853378","price":168.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521853370.jpg?v=1751103864","url":"https:\/\/www.worldofbooks.com\/en-gb\/products\/free-ideal-rings-and-localization-in-general-rings-book-p-m-cohn-9780521853378","provider":"World of Books ","version":"1.0","type":"link"}