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Titlebook: Ring Theory; Dinesh Khattar,Neha Agrawal Textbook 2023 The Author(s) 2023 Simple Rings.Factor Rings.Ring Homomorphisms.Isomorphisms.Ring H

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樓主
發(fā)表于 2025-3-21 20:08:02 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Ring Theory
編輯Dinesh Khattar,Neha Agrawal
視頻videohttp://file.papertrans.cn/831/830410/830410.mp4
概述Contains full details of all proofs which are included along with innumerous solved problems.Offers proofs which are precise and complete, backed up by chapter end problems, with just the right level
圖書封面Titlebook: Ring Theory;  Dinesh Khattar,Neha Agrawal Textbook 2023 The Author(s) 2023 Simple Rings.Factor Rings.Ring Homomorphisms.Isomorphisms.Ring H
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..
出版日期Textbook 2023
關(guān)鍵詞Simple Rings; Factor Rings; Ring Homomorphisms; Isomorphisms; Ring Homomorphism; Isomorphism Theorems; Pol
版次1
doihttps://doi.org/10.1007/978-3-031-29440-2
isbn_softcover978-3-031-29442-6
isbn_ebook978-3-031-29440-2
copyrightThe Author(s) 2023
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 21:16:10 | 只看該作者
Ideals and Factor Rings,pecial case of normal subgroups. There is a neat structural parallel to be drawn here the notion of an ideal in a ring is analogous to the concept of a normal subgroup in groups. The similarities do not end here! Just as normal subgroups led us to the creation of quotient groups, in a similar way id
板凳
發(fā)表于 2025-3-22 01:59:41 | 只看該作者
Ring Homomorphisms and Isomorphisms,ur journey deeper into ring theory shall pass through the borderlands of groups. Why? Because the homomorphisms and isomorphisms of rings are exactly analogous to the notions of homomorphisms and isomorphisms in groups! Only a little tweaking is required to move the concept from groups to rings. Hom
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發(fā)表于 2025-3-22 18:57:13 | 只看該作者
Ring Homomorphisms and Isomorphisms,ism between two rings which preserves both the binary operations. In other words, a ring homomorphism is a structure-preserving function between two rings. So, just as Group theory requires us to look at maps which “preserve the operation”, Ring theory demands that we look at maps which preserve both operations.
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發(fā)表于 2025-3-23 00:37:02 | 只看該作者
Divisibility in Integral Domains,nd the Euclidean domains, along with their distinctive properties. The definition of the unique factorization domain arises as an application of the fundamental theorem of arithmetic, which is true in the ring of integers, to more abstract rings.
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發(fā)表于 2025-3-23 06:37:31 | 只看該作者
Polynomial Rings,als—that is, as mathematical expressions consisting of variables, coefficients, and the operations of addition, subtraction, multiplication, and non-negative integer exponents. This is familiar territory. Let us now travel to uncharted lands.
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