Semigroups and Their Subsemigroup Lattices
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1996
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| Schriftenreihe: | Mathematics and Its Applications
379 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| 100 | 1 | |a Shevrin, Lev N. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Semigroups and Their Subsemigroup Lattices |c by Lev N. Shevrin, Alexander J. Ovsyannikov |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1996 | |
| 300 | |a 1 Online-Ressource (XI, 380 p) | ||
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| 490 | 0 | |a Mathematics and Its Applications |v 379 | |
| 500 | |a 0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A partially ordered by inclusion forms a lattice. This is the subsystem lattice of A. (In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years. This trend was formed first in group theory; basic relevant information up to the early seventies is contained in the book [Suz] and the surveys [K Pek St], [Sad 2], [Ar Sad], there is also a quite recent book [Schm 2]. As another inspiring source, one should point out a branch of mathematics to which the book [Baer] was devoted. One of the key objects of examination in this branch is the subspace lattice of a vector space over a skew field. A more general approach deals with modules and their submodule lattices. Examining subsystem lattices for the case of modules as well as for rings and algebras (both associative and non-associative, in particular, Lie algebras) began more than thirty years ago; there are results on this subject also for lattices, Boolean algebras and some other types of algebraic systems, both concrete and general. A lot of works including several surveys have been published here | ||
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| 650 | 4 | |a Order, Lattices, Ordered Algebraic Structures | |
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Datensatz im Suchindex
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|---|---|
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| author | Shevrin, Lev N. |
| author_facet | Shevrin, Lev N. |
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| author_sort | Shevrin, Lev N. |
| author_variant | l n s ln lns |
| building | Verbundindex |
| bvnumber | BV042424083 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184494379 (DE-599)BVBBV042424083 |
| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8751-8 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-12-24T04:23:29Z |
| institution | BVB |
| isbn | 9789401587518 9789048147496 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859500 |
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| physical | 1 Online-Ressource (XI, 380 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1996 |
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| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications |
| spelling | Shevrin, Lev N. Verfasser aut Semigroups and Their Subsemigroup Lattices by Lev N. Shevrin, Alexander J. Ovsyannikov Dordrecht Springer Netherlands 1996 1 Online-Ressource (XI, 380 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 379 0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A partially ordered by inclusion forms a lattice. This is the subsystem lattice of A. (In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years. This trend was formed first in group theory; basic relevant information up to the early seventies is contained in the book [Suz] and the surveys [K Pek St], [Sad 2], [Ar Sad], there is also a quite recent book [Schm 2]. As another inspiring source, one should point out a branch of mathematics to which the book [Baer] was devoted. One of the key objects of examination in this branch is the subspace lattice of a vector space over a skew field. A more general approach deals with modules and their submodule lattices. Examining subsystem lattices for the case of modules as well as for rings and algebras (both associative and non-associative, in particular, Lie algebras) began more than thirty years ago; there are results on this subject also for lattices, Boolean algebras and some other types of algebraic systems, both concrete and general. A lot of works including several surveys have been published here Mathematics Group theory Algebra Logic, Symbolic and mathematical Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Mathematik Unterhalbgruppe (DE-588)4186987-4 gnd rswk-swf Halbgruppe (DE-588)4022990-7 gnd rswk-swf Verband Mathematik (DE-588)4062565-5 gnd rswk-swf Halbgruppe (DE-588)4022990-7 s Unterhalbgruppe (DE-588)4186987-4 s Verband Mathematik (DE-588)4062565-5 s 1\p DE-604 Ovsyannikov, Alexander J. Sonstige oth https://doi.org/10.1007/978-94-015-8751-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shevrin, Lev N. Semigroups and Their Subsemigroup Lattices Mathematics Group theory Algebra Logic, Symbolic and mathematical Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Mathematik Unterhalbgruppe (DE-588)4186987-4 gnd Halbgruppe (DE-588)4022990-7 gnd Verband Mathematik (DE-588)4062565-5 gnd |
| subject_GND | (DE-588)4186987-4 (DE-588)4022990-7 (DE-588)4062565-5 |
| title | Semigroups and Their Subsemigroup Lattices |
| title_auth | Semigroups and Their Subsemigroup Lattices |
| title_exact_search | Semigroups and Their Subsemigroup Lattices |
| title_full | Semigroups and Their Subsemigroup Lattices by Lev N. Shevrin, Alexander J. Ovsyannikov |
| title_fullStr | Semigroups and Their Subsemigroup Lattices by Lev N. Shevrin, Alexander J. Ovsyannikov |
| title_full_unstemmed | Semigroups and Their Subsemigroup Lattices by Lev N. Shevrin, Alexander J. Ovsyannikov |
| title_short | Semigroups and Their Subsemigroup Lattices |
| title_sort | semigroups and their subsemigroup lattices |
| topic | Mathematics Group theory Algebra Logic, Symbolic and mathematical Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Mathematik Unterhalbgruppe (DE-588)4186987-4 gnd Halbgruppe (DE-588)4022990-7 gnd Verband Mathematik (DE-588)4062565-5 gnd |
| topic_facet | Mathematics Group theory Algebra Logic, Symbolic and mathematical Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Mathematik Unterhalbgruppe Halbgruppe Verband Mathematik |
| url | https://doi.org/10.1007/978-94-015-8751-8 |
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