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Introduction to Modern Algebra - Clark University

Introduction to Modern AlgebraDavid JoyceClark UniversityVersion , 5 Dec 201711 Copyright (C) 2008, dedicate this book to my friend and colleague Arthur Chou. Arthur encouraged me to writethis book. I m sorry that he did not live to see it was born in 1954 in Taipei, Taiwan. He received his bachelors in mathematicsin 1976 from Tunghai University and his PhD from Stony Brook in 1982. After a year atthe Institute for Advanced Study at Princeton, he joined Clark University in 1983. He waspromoted to Associate Professor six years later and promoted to full professor in 2008, theyear he died. Besides mathematics, he had many other interests. Among other things, he wasthe general manager of the North America Elite Youth Orchestra which performed at Dallas,Beijing, and Taipei, and he was the deacon of the Chinese Gospel Church in Southborough, of FiguresviList of Tablesviii1 Algebra .

the eld of rational number, and the eld of complex numbers, but there was no general de nition for a eld until the late 1800s. (See chapter2for elds.) Rings also were studied in the 1800s. Noether (1882{1935) gave general concept of com-mutative ring in 1921 which was later generalized to include noncommutative rings. (See 1

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