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On the one hand this book intends to provide an introduction to module theory and the related part of ring theory. Topics covered includes: Elementary properties of rings, Module categories, Modules characterized by the Hom-functor, Notions derived from simple modules, Finiteness conditions in modules, Dual finiteness conditions, Pure sequences and derived notions, Relations between functors and Functor rings.
Author(s): Robert Wisbauer
616Pages
This wikibook explains ring theory. Topics covered includes: Rings, Properties of rings, Integral domains and Fields, Subrings, Idempotent and Nilpotent elements, Characteristic of a ring, Ideals in a ring, Simple ring, Homomorphisms, Principal Ideal Domains, Euclidean domains, Polynomial rings, Unique Factorization domain, Extension fields.
Author(s): wikibook
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Aim of this book is to help the students by giving them some exercises and get them familiar with some solutions. Some of the solutions here are very short and in the form of a hint. Topics covered includes: Sets, Integers, Functions, Groups, Rings and Fields.
Author(s): Mahmut Kuzucuoglu
106Pages
This note covers the following topics: Rings: Definition, examples and elementary properties, Ideals and ring homomorphisms, Polynomials, unique factorisation, Factorisation of polynomials, Prime and maximal ideals, Fields, Motivatie Galoistheorie, Splitting fields and Galois groups, The Main Theorem of Galois theory, Solving equation and Finite fields.
Author(s): F.Beuker
121Pages
This note covers the following topics: Introduction to number rings, Ideal arithmetic, Explicit ideal factorization, Linear algebra for number rings, Geometry of numbers, Zeta functions, Computing units and class groups, Galois theory for number fields.
Author(s): Stevenhagen
84Pages
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