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

Limbic-System

书目名称Ring Theory影响因子(影响力)




书目名称Ring Theory影响因子(影响力)学科排名




书目名称Ring Theory网络公开度




书目名称Ring Theory网络公开度学科排名




书目名称Ring Theory被引频次




书目名称Ring Theory被引频次学科排名




书目名称Ring Theory年度引用




书目名称Ring Theory年度引用学科排名




书目名称Ring Theory读者反馈




书目名称Ring Theory读者反馈学科排名

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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

Incorporate

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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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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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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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.