{"product_id":"fields-and-rings-chicago-lectures-in-mathematics-9780226424514","title":"Fields and Rings Chicago Lectures in Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface Pt. I: Fields 1: Field extensions 2: Ruler and compass constructions 3: Foundations of Galois theory 4: Normality and stability 5: Splitting fields 6: Radical extensions 7: The trace and norm theorems 8: Finite fields 9: Simple extensions 10: Cubic and quartic equations 11: Separability 12: Miscellaneous results on radical extensions 13: Infinite algebraic extensions Pt. II: Rings 1: The radical 2: Primitive rings and the density theorem 3: Semi-simple rings 4: The Wedderburn principal theorem 5: Theorems of Hopkins and Levitzki 6: Primitive rings with minimal ideals and dual vector spaces 7: Simple rings Pt. III: Homological Dimension 1: Dimension of modules 2: Global dimension 3: First theorem on change of rings 4: Polynomial rings 5: Second theorem on change of rings 6: Third theorem on change of rings 7: Localization 8: Preliminary lemmas 9: A regular ring has finite global dimension 10: A local ring of finite global dimension is regular 11: Injective modules 12: The group of homomorphisms 13: The vanishing of Ext 14: Injective dimension Notes Index","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":49400017387863,"sku":"9780226424514","price":30.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226424514.jpg?v=1730469457","url":"https:\/\/bookcurl.com\/products\/fields-and-rings-chicago-lectures-in-mathematics-9780226424514","provider":"Book Curl","version":"1.0","type":"link"}