Foundations of module and ring theory : a handbook for study and research
著者
書誌事項
Foundations of module and ring theory : a handbook for study and research
（Algebra, logic and applications series, v. 3）
Gordon and Breach Science Publishers, c1991
Rev. and updated English ed.
- タイトル別名
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Grundlagen der Modul- und Ringtheorie
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注記
Includes bibliographical references (p. 576-598) and index
内容説明・目次
内容説明
This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
目次
1. Elementary properties of rings 2. Module categories 3. Modules characterized by the Hom-functor 4. Notions derived from simple modules 5. Finiteness conditions in modules 6. Dual finiteness conditions 7. pure sequences and derived notions 8. Modules described by means of projectivity 9. Relations between functors 10. Functor Rings
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