Semidistributive Modules and Rings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1998
|
| Schriftenreihe: | Mathematics and Its Applications
449 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A module M is called distributive if the lattice Lat(M) of all its submodules is distributive, i.e., Fn(G + H) = FnG + FnH for all submodules F,G, and H of the module M. A module M is called uniserial if all its submodules are comparable with respect to inclusion, i.e., the lattice Lat(M) is a chain. Any direct sum of distributive (resp. uniserial) modules is called a semidistributive (resp. serial) module. The class of distributive (resp. semidistributive) modules properly cont.ains the class ofall uniserial (resp. serial) modules. In particular, all simple (resp. semisimple) modules are distributive (resp. semidistributive). All strongly regular rings (for example, all factor rings of direct products of division rings and all commutative regular rings) are distributive; all valuation rings in division rings and all commutative Dedekind rings (e.g., rings of integral algebraic numbers or commutative principal ideal rings) are distributive. A module is called a Bezout module or a locally cyclic module ifevery finitely generated submodule is cyclic. If all maximal right ideals of a ring A are ideals (e.g., if A is commutative), then all Bezout A-modules are distributive |
| Beschreibung: | 1 Online-Ressource (X, 357 p) |
| ISBN: | 9789401150866 9789401061360 |
| DOI: | 10.1007/978-94-011-5086-6 |
Internformat
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| 490 | 0 | |a Mathematics and Its Applications |v 449 | |
| 500 | |a A module M is called distributive if the lattice Lat(M) of all its submodules is distributive, i.e., Fn(G + H) = FnG + FnH for all submodules F,G, and H of the module M. A module M is called uniserial if all its submodules are comparable with respect to inclusion, i.e., the lattice Lat(M) is a chain. Any direct sum of distributive (resp. uniserial) modules is called a semidistributive (resp. serial) module. The class of distributive (resp. semidistributive) modules properly cont.ains the class ofall uniserial (resp. serial) modules. In particular, all simple (resp. semisimple) modules are distributive (resp. semidistributive). All strongly regular rings (for example, all factor rings of direct products of division rings and all commutative regular rings) are distributive; all valuation rings in division rings and all commutative Dedekind rings (e.g., rings of integral algebraic numbers or commutative principal ideal rings) are distributive. A module is called a Bezout module or a locally cyclic module ifevery finitely generated submodule is cyclic. If all maximal right ideals of a ring A are ideals (e.g., if A is commutative), then all Bezout A-modules are distributive | ||
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| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Associative Rings and Algebras | |
| 650 | 4 | |a Commutative Rings and Algebras | |
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Datensatz im Suchindex
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401150866 9789401061360 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859382 |
| oclc_num | 863694112 |
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| physical | 1 Online-Ressource (X, 357 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Springer Netherlands |
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| series2 | Mathematics and Its Applications |
| spelling | Tuganbaev, Askar A. Verfasser aut Semidistributive Modules and Rings by Askar A. Tuganbaev Dordrecht Springer Netherlands 1998 1 Online-Ressource (X, 357 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 449 A module M is called distributive if the lattice Lat(M) of all its submodules is distributive, i.e., Fn(G + H) = FnG + FnH for all submodules F,G, and H of the module M. A module M is called uniserial if all its submodules are comparable with respect to inclusion, i.e., the lattice Lat(M) is a chain. Any direct sum of distributive (resp. uniserial) modules is called a semidistributive (resp. serial) module. The class of distributive (resp. semidistributive) modules properly cont.ains the class ofall uniserial (resp. serial) modules. In particular, all simple (resp. semisimple) modules are distributive (resp. semidistributive). All strongly regular rings (for example, all factor rings of direct products of division rings and all commutative regular rings) are distributive; all valuation rings in division rings and all commutative Dedekind rings (e.g., rings of integral algebraic numbers or commutative principal ideal rings) are distributive. A module is called a Bezout module or a locally cyclic module ifevery finitely generated submodule is cyclic. If all maximal right ideals of a ring A are ideals (e.g., if A is commutative), then all Bezout A-modules are distributive Mathematics Algebra Associative Rings and Algebras Commutative Rings and Algebras Mathematik https://doi.org/10.1007/978-94-011-5086-6 Verlag Volltext |
| spellingShingle | Tuganbaev, Askar A. Semidistributive Modules and Rings Mathematics Algebra Associative Rings and Algebras Commutative Rings and Algebras Mathematik |
| title | Semidistributive Modules and Rings |
| title_auth | Semidistributive Modules and Rings |
| title_exact_search | Semidistributive Modules and Rings |
| title_full | Semidistributive Modules and Rings by Askar A. Tuganbaev |
| title_fullStr | Semidistributive Modules and Rings by Askar A. Tuganbaev |
| title_full_unstemmed | Semidistributive Modules and Rings by Askar A. Tuganbaev |
| title_short | Semidistributive Modules and Rings |
| title_sort | semidistributive modules and rings |
| topic | Mathematics Algebra Associative Rings and Algebras Commutative Rings and Algebras Mathematik |
| topic_facet | Mathematics Algebra Associative Rings and Algebras Commutative Rings and Algebras Mathematik |
| url | https://doi.org/10.1007/978-94-011-5086-6 |
| work_keys_str_mv | AT tuganbaevaskara semidistributivemodulesandrings |