書目名稱 | Rings, Modules, and the Total | 編輯 | Friedrich Kasch,Adolf Mader | 視頻video | http://file.papertrans.cn/831/830428/830428.mp4 | 概述 | Accessible to anyone with a basic knowledge of ring and module theory.A short introduction to torsion-free Abelian groups is included | 叢書名稱 | Frontiers in Mathematics | 圖書封面 |  | 描述 | .In a nutshell, the book deals with direct decompositions of modules and associated concepts. The central notion of "partially invertible homomorphisms”, namely those that are factors of a non-zero idempotent, is introduced in a very accessible fashion. Units and regular elements are partially invertible. The "total” consists of all elements that are not partially invertible. The total contains the radical and the singular and cosingular submodules, but while the total is closed under right and left multiplication, it may not be closed under addition. Cases are discussed where the total is additively closed. The total is particularly suited to deal with the endomorphism ring of?the direct sum of modules that all have local endomorphism rings and is applied in this case. Further applications are given for torsion-free Abelian groups.. | 出版日期 | Book 2004 | 關(guān)鍵詞 | Algebra; Group Theory; Modules; Rings; Abelian group; algebra; endomorphism ring; Group theory; homomorphism | 版次 | 1 | doi | https://doi.org/10.1007/b96769 | isbn_softcover | 978-3-7643-7125-8 | isbn_ebook | 978-3-7643-7801-1Series ISSN 1660-8046 Series E-ISSN 1660-8054 | issn_series | 1660-8046 | copyright | Springer Basel AG 2004 |
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