Endomorphism Rings of Abelian Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2003
|
| Schriftenreihe: | Algebras and Applications
2 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomorphism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information about Abelian groups themselves, to introduce new concepts and methods, and to find new interesting classes of groups; second, it stimulates further development of the theory of modules and their endomorphism rings. The theory of endomorphism rings can also be useful for studies of the structure of additive groups of rings, E-modules, and homological properties of Abelian groups. The books of Baer [52] and Kaplansky [245] have played an important role in the early development of the theory of endomorphism rings of Abelian groups and modules. Endomorphism rings of Abelian groups are much studied in monographs of Fuchs [170], [172], and [173]. Endomorphism rings are also studied in the works of Kurosh [287], Arnold [31], and Benabdallah [63] |
| Beschreibung: | 1 Online-Ressource (XII, 443 p) |
| ISBN: | 9789401703451 9789048163496 |
| ISSN: | 1572-5553 |
| DOI: | 10.1007/978-94-017-0345-1 |
Internformat
MARC
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| 245 | 1 | 0 | |a Endomorphism Rings of Abelian Groups |c by Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 2003 | |
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| 490 | 1 | |a Algebras and Applications |v 2 |x 1572-5553 | |
| 500 | |a Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomorphism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information about Abelian groups themselves, to introduce new concepts and methods, and to find new interesting classes of groups; second, it stimulates further development of the theory of modules and their endomorphism rings. The theory of endomorphism rings can also be useful for studies of the structure of additive groups of rings, E-modules, and homological properties of Abelian groups. The books of Baer [52] and Kaplansky [245] have played an important role in the early development of the theory of endomorphism rings of Abelian groups and modules. Endomorphism rings of Abelian groups are much studied in monographs of Fuchs [170], [172], and [173]. Endomorphism rings are also studied in the works of Kurosh [287], Arnold [31], and Benabdallah [63] | ||
| 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 Commutative Rings and Algebras | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a Mikhalev, Aleksandr Vasilʹevič |d 1940- |e Sonstige |0 (DE-588)1089283873 |4 oth | |
| 700 | 1 | |a Tuganbaev, Askar A. |e Sonstige |0 (DE-588)103454148X |4 oth | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Krylov, Petr Andreevič |
| author_GND | (DE-588)106838090X (DE-588)1089283873 (DE-588)103454148X |
| author_facet | Krylov, Petr Andreevič |
| author_role | aut |
| author_sort | Krylov, Petr Andreevič |
| author_variant | p a k pa pak |
| building | Verbundindex |
| bvnumber | BV042424201 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)860051008 (DE-599)BVBBV042424201 |
| dewey-full | 512.46 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.46 |
| dewey-search | 512.46 |
| dewey-sort | 3512.46 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-0345-1 |
| format | Electronic eBook |
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| id | DE-604.BV042424201 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401703451 9789048163496 |
| issn | 1572-5553 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859618 |
| oclc_num | 860051008 |
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| physical | 1 Online-Ressource (XII, 443 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2003 |
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| publisher | Springer Netherlands |
| record_format | marc |
| series | Algebras and Applications |
| series2 | Algebras and Applications |
| spelling | Krylov, Petr Andreevič Verfasser (DE-588)106838090X aut Endomorphism Rings of Abelian Groups by Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev Dordrecht Springer Netherlands 2003 1 Online-Ressource (XII, 443 p) txt rdacontent c rdamedia cr rdacarrier Algebras and Applications 2 1572-5553 Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomorphism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information about Abelian groups themselves, to introduce new concepts and methods, and to find new interesting classes of groups; second, it stimulates further development of the theory of modules and their endomorphism rings. The theory of endomorphism rings can also be useful for studies of the structure of additive groups of rings, E-modules, and homological properties of Abelian groups. The books of Baer [52] and Kaplansky [245] have played an important role in the early development of the theory of endomorphism rings of Abelian groups and modules. Endomorphism rings of Abelian groups are much studied in monographs of Fuchs [170], [172], and [173]. Endomorphism rings are also studied in the works of Kurosh [287], Arnold [31], and Benabdallah [63] Mathematics Algebra Group theory Associative Rings and Algebras Group Theory and Generalizations Commutative Rings and Algebras Mathematik Mikhalev, Aleksandr Vasilʹevič 1940- Sonstige (DE-588)1089283873 oth Tuganbaev, Askar A. Sonstige (DE-588)103454148X oth Algebras and Applications 2 (DE-604)BV035420975 2 https://doi.org/10.1007/978-94-017-0345-1 Verlag Volltext |
| spellingShingle | Krylov, Petr Andreevič Endomorphism Rings of Abelian Groups Algebras and Applications Mathematics Algebra Group theory Associative Rings and Algebras Group Theory and Generalizations Commutative Rings and Algebras Mathematik |
| title | Endomorphism Rings of Abelian Groups |
| title_auth | Endomorphism Rings of Abelian Groups |
| title_exact_search | Endomorphism Rings of Abelian Groups |
| title_full | Endomorphism Rings of Abelian Groups by Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev |
| title_fullStr | Endomorphism Rings of Abelian Groups by Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev |
| title_full_unstemmed | Endomorphism Rings of Abelian Groups by Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev |
| title_short | Endomorphism Rings of Abelian Groups |
| title_sort | endomorphism rings of abelian groups |
| topic | Mathematics Algebra Group theory Associative Rings and Algebras Group Theory and Generalizations Commutative Rings and Algebras Mathematik |
| topic_facet | Mathematics Algebra Group theory Associative Rings and Algebras Group Theory and Generalizations Commutative Rings and Algebras Mathematik |
| url | https://doi.org/10.1007/978-94-017-0345-1 |
| volume_link | (DE-604)BV035420975 |
| work_keys_str_mv | AT krylovpetrandreevic endomorphismringsofabeliangroups AT mikhalevaleksandrvasilʹevic endomorphismringsofabeliangroups AT tuganbaevaskara endomorphismringsofabeliangroups |