01987    a2200289   4500001001100000005001700011008003900028020002200067037003600089040000700125041000800132072001500140072001500155072001300170072001300183072002100196072002100217072001700238100002200255245003900277250000600316260003500322300001000357520129500367700002001662999001501682104029821420250328151419.0250324042025xx                   eng    a9781040298213qEA  bTaylor & FranciscGBP 91.99fBB  a01  aeng7 aPBF2thema7 aPBG2thema7 aPBF2bic7 aPBG2bic7 aMAT0000002bisac7 aMAT0020002bisac7 a512.92bisac1 aLouis Halle Rowen10aAlgebrabGroups, Rings, and Fields  a2  bChapman and Hall/CRCc20250221  a374 p  bAlgebra is a subject we have become acquainted with during most of our mathematical education, often in connection with the solution of equations. Algebra: Groups, Rings, and Fields, Second Edition deals with developments related to their solutions. The principle at the heart of abstract algebra, a subject that enables one to deduce sweeping conclusions from elementary premises, is that the process of abstraction enables us to solve a variety of such problems with economy of effort. This leads to the glorious world of mathematical discovery. This second edition follows the original three-pronged approach: the theory of finite groups, number theory, and Galois’ amazing theory of field extensions tying solvability of equations to group theory. As algebra has branched out in many directions, the authors strive to keep the text manageable while at the same time introducing the student to exciting new paths. In order to support this approach, the authors broadened the first edition, giving monoids a greater role, and relying more on matrices. Hundreds of new exercises were added. A course in abstract algebra, properly presented, could treat mathematics as an art as well as a science. In this exposition, we try to present underlying ideas, as well as the results they yield.1 aUzi Vishne4A01  c8016d8016