{"product_id":"free-ideal-rings-and-localization-in-general-rings-9780521853378","title":"Free Ideal Rings and Localization in General Rings","description":"\u003cp\u003e • Author(s): P. M. Cohn\u003cbr\u003e • Publisher: Cambridge University Press\u003cbr\u003e • Publisher Imprint: Cambridge University Press\u003cbr\u003e • BISAC: Algebra - General\u003c\/p\u003e\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. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention.\u003c\/p\u003e","brand":"Cambridge University Press","offers":[{"title":"Hardcover","offer_id":46432946847895,"sku":"9780521853378","price":13327.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780521853378.webp?v=1769306852","url":"https:\/\/atlanticbooks.com\/products\/free-ideal-rings-and-localization-in-general-rings-9780521853378","provider":"Atlantic Books","version":"1.0","type":"link"}