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商品描述
This textbook is designed for the UG/PG students of mathematics for all universities over the world. It is primarily based on the classroom lectures, the authors gave at the University of Delhi. This book is used both for self-study and course text. Full details of all proofs are included along with innumerous solved problems, interspersed throughout the text and at places where they naturally arise, to understand abstract notions. The proofs are precise and complete, backed up by chapter end problems, with just the right level of difficulty, without compromising the rigor of the subject. The book starts with definition and examples of Rings and logically follows to cover Properties of Rings, Subrings, Fields, Characteristic of a Ring, Ideals, Integral Domains, Factor Rings, Prime Ideals, Maximal Ideals and Primary Ideals, Ring Homomorphisms and Isomorphisms, Polynomial Rings, Factorization of Polynomials, and Divisibility in Integral Domains.
商品描述(中文翻譯)
這本教科書是為全球所有大學的數學本科生和研究生設計的。它主要基於作者在德里大學的課堂講座。本書既可用於自學，也可作為課程教材。書中包含所有證明的詳細內容，並穿插了無數的解題，這些解題在文本中自然出現，以幫助理解抽象概念。證明精確且完整，並附有章末問題，難度適中，且不妥協於學科的嚴謹性。本書從環（Rings）的定義和例子開始，邏輯性地涵蓋環的性質、子環（Subrings）、域（Fields）、環的特徵（Characteristic of a Ring）、理想（Ideals）、整數域（Integral Domains）、因子環（Factor Rings）、質理想（Prime Ideals）、極大理想（Maximal Ideals）和初級理想（Primary Ideals）、環同態（Ring Homomorphisms）和同構（Isomorphisms）、多項式環（Polynomial Rings）、多項式的因式分解（Factorization of Polynomials）以及整數域中的可除性（Divisibility in Integral Domains）。
作者簡介
Prof. Dinesh Khattar is currently principal of Kirori Mal College, University of Delhi. He topped (Gold Medalist) both in his B.Sc. and M.Sc. exams of Delhi University. He received Dr. S. Radhakrishnan Memorial National Teacher's Award 2015 for his contribution in the field of education. He was also awarded the prestigious Commonwealth Scholarship for pursuing research in the UK. He is actively involved in research and has presented papers in prestigious international conferences across the globe. Dr. Khattar has been a member of curriculum development committee for B.Sc. and M.Sc. programs at various universities including the University of Delhi. He is also an author of many books on Mathematics.
Dr. Neha Agrawal completed her education from Kirori Mal College, University of Delhi, and pursued her M.Phil. and Ph.D. from University of Delhi. Her areas of interest are nonlinear dynamical systems and chaos theory. She is working as an assistant professor at the Department ofMathematics, Kirori Mal College, University of Delhi. She has a rich teaching experience of over 13 years. She has published several research papers in reputed international journals.
作者簡介(中文翻譯)
教授 Dinesh Khattar 目前是德里大學 Kirori Mal 學院的院長。他在德里大學的學士和碩士考試中均名列前茅（獲得金獎）。他因在教育領域的貢獻而獲得 2015 年 Dr. S. Radhakrishnan 紀念全國教師獎。他還獲得了享有盛譽的英聯邦獎學金，以便在英國進行研究。他積極參與研究，並在全球多個享有盛譽的國際會議上發表論文。Khattar 博士曾擔任多所大學（包括德里大學）學士和碩士課程的課程發展委員會成員。他也是多本數學書籍的作者。
Neha Agrawal 博士在德里大學的 Kirori Mal 學院完成了她的學業，並在德里大學獲得了 M.Phil. 和 Ph.D. 學位。她的研究興趣包括非線性動力系統和混沌理論。她目前在德里大學 Kirori Mal 學院的數學系擔任助理教授，擁有超過 13 年的豐富教學經驗。她在多本知名國際期刊上發表了幾篇研究論文。
