Rings, Modules, and the Total:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2004
|
| Schriftenreihe: | Frontiers in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (X, 138 p) |
| ISBN: | 9783764378011 9783764371258 |
| ISSN: | 1660-8046 |
| DOI: | 10.1007/b96769 |
Internformat
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| 490 | 0 | |a Frontiers in Mathematics |x 1660-8046 | |
| 500 | |a 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Associative Rings and Algebras | |
| 650 | 4 | |a Group Theory and Generalizations | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a Mader, Adolf |e Sonstige |4 oth | |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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| id | DE-604.BV042423584 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783764378011 9783764371258 |
| issn | 1660-8046 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859001 |
| oclc_num | 845873840 |
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| physical | 1 Online-Ressource (X, 138 p) |
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| publishDate | 2004 |
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| publisher | Birkhäuser Basel |
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| series2 | Frontiers in Mathematics |
| spelling | Kasch, Friedrich Verfasser aut Rings, Modules, and the Total by Friedrich Kasch, Adolf Mader Basel Birkhäuser Basel 2004 1 Online-Ressource (X, 138 p) txt rdacontent c rdamedia cr rdacarrier Frontiers in Mathematics 1660-8046 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 Mathematics Algebra Group theory Associative Rings and Algebras Group Theory and Generalizations Mathematik Mader, Adolf Sonstige oth https://doi.org/10.1007/b96769 Verlag Volltext |
| spellingShingle | Kasch, Friedrich Rings, Modules, and the Total Mathematics Algebra Group theory Associative Rings and Algebras Group Theory and Generalizations Mathematik |
| title | Rings, Modules, and the Total |
| title_auth | Rings, Modules, and the Total |
| title_exact_search | Rings, Modules, and the Total |
| title_full | Rings, Modules, and the Total by Friedrich Kasch, Adolf Mader |
| title_fullStr | Rings, Modules, and the Total by Friedrich Kasch, Adolf Mader |
| title_full_unstemmed | Rings, Modules, and the Total by Friedrich Kasch, Adolf Mader |
| title_short | Rings, Modules, and the Total |
| title_sort | rings modules and the total |
| topic | Mathematics Algebra Group theory Associative Rings and Algebras Group Theory and Generalizations Mathematik |
| topic_facet | Mathematics Algebra Group theory Associative Rings and Algebras Group Theory and Generalizations Mathematik |
| url | https://doi.org/10.1007/b96769 |
| work_keys_str_mv | AT kaschfriedrich ringsmodulesandthetotal AT maderadolf ringsmodulesandthetotal |