数论基础(英文版)(ELEMENTS OF NUMBER THEORY)
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品牌: 史迪威
基本信息·出版社：世界图书出版公司
·页码：254 页
·出版日期：2009年
·ISBN：7510004675/9787510004674
·条形码：9787510004674
·包装版本：1版
·装帧：平装
·开本：24
·正文语种：英语
·外文书名：ELEMENTS OF NUMBER THEORY
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内容简介《数论基础(英文版)》内容为：This book is intended to complement my Elements of Algebra, and it is similarly motivated by the problem of solving polynomial equations.However, it is independent of the algebra book, and probably easier. In Elements of Algebra we sought solution by radicals, and this led to theconcepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theo of ideals due to Kummer and Dedekind.
编辑推荐《数论基础(英文版)》由史迪威所著。
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序言This book is intended to complement my Elements of Algebra, and itis similarly motivated by the problem of solving polynomial equations.However, it is independent of the algebra book, and probably easier. InElements of Algebra we sought solution by radicals, and this led to theconcepts of fields and groups and their fusion in the celebrated theory ofGalois. In the present book we seek integer solutions, and this leads to theconcepts of rings and ideals which merge in the equally celebrated theol.of ideals due to Kummer and Dedekind.
Solving equations in integers is the central problem of number theory,so this book is truly a number theory book, with most of the results foundin standard number theory courses. However, numbers are best understoodthrough their algebraic structure, and the necessary algebraic concepts rings and ideals have no better motivation than number theory.
The first nontrivial examples of rings appear in the number theoryof Euler and Gauss. The concept of ideal today as routine in ring theory as the concept of normal subgroup is in group theory also emergedfrom number theory, and in quite heroic fashion. Faced with failure ofunique prime factorization in the arithmetic of certain generalized "integers", Kummer created in the 1840s a new kind of number to overcomethe difficulty. He called them "ideal numbers" because he did not knowexactly what they were, though he knew how they behaved. Dedekind in1871 found that these "ideal numbers" could be realized as sets of actualnumbers, and he called these sets ideals.
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