{"product_id":"9780521853378","title":"Free Ideal Rings and Localization in General Rings (New Mathematical Monographs)","description":"\u003cp\u003eProving 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.\u003c\/p\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":49108116242659,"sku":"00000_00000_00000_00000","price":228.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0764\/3758\/6147\/files\/9780521853378-1.jpg?v=1788343835","url":"https:\/\/usa.kinokuniya.com\/ja\/products\/9780521853378","provider":"Books Kinokuniya USA","version":"1.0","type":"link"}