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N-gons.
This book, a translation of the German volume€ n-Ecke, presents an elegant geometric theory which, starting from quite elementary geometrical observations, exhibits an interesting connection between geometry and fundamental ideas of modern algebra.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Toronto :
University of Toronto Press,
1975.
|
| Colección: | Heritage.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Mu 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn958557737 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr |n|---||||| | ||
| 008 | 160917s1975 onc o 000 0 eng d | ||
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| 066 | |c (S | ||
| 020 | |a 9781442656444 | ||
| 020 | |a 1442656441 | ||
| 020 | |a 9781442651548 | ||
| 020 | |a 1442651547 | ||
| 020 | |a 9780802018434 | ||
| 020 | |a 0802018432 | ||
| 029 | 1 | |a AU@ |b 000074667236 | |
| 035 | |a (OCoLC)958557737 | ||
| 050 | 4 | |a QA482 |b .B334 1975 | |
| 082 | 0 | 4 | |a 516/.22 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Bachmann, Friedrich. | |
| 245 | 1 | 0 | |a N-gons. |
| 260 | |a Toronto : |b University of Toronto Press, |c 1975. | ||
| 300 | |a 1 online resource (208 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Heritage | |
| 588 | 0 | |a Print version record. | |
| 520 | |a This book, a translation of the German volume€ n-Ecke, presents an elegant geometric theory which, starting from quite elementary geometrical observations, exhibits an interesting connection between geometry and fundamental ideas of modern algebra. | ||
| 505 | 8 | |6 880-01 |a 3 A special case of idempotent-transfer -- 4 Ideals and divisibility in a principal ideal domain -- 5 Residue class rings of principal ideal domains -- 6 Residue class rings as sums of residue class rings -- 8 Boolean algebras of the w-gonal theory I -- 1 The Boolean algebras L₁-L₅ -- 2 Divisors of x[sup(n)] -- 1 and cyclic classes -- 3 Spectrum -- 4 Examples of defining cyclic classes by divisors of xⁿ -1 -- 9 Boolean algebras of the n-gonal theory II -- 1 Galois correspondence of annihilators and kernels -- 2 Ideal-transfer -- 3 Second proof of the main theorem: Main diagram -- 4 Graduation: Degree of freedom of a cyclic class -- 5 Miscellaneous exercises -- PART IV: Atomic decompositions -- 10 Rational components of an n-gon -- 1 Q-regular n-gons -- 2 Cyclic classes defined by cyclotomic polynomials -- 3 Rational components of an n-gon -- 4 The Boolean algebra generated by omitting averaging projections and its atoms -- 5 Construction of the rational components of an n-gon -- 11 Complex components of an n-gon -- 1 w-n-gons, regular n-gons -- 2 The case of the complex field -- 3 Complex components of an n-gon -- 12 The real components of an n-gon -- 1 Anticyclic cyclic classes -- 2 A special type of cyclic systems of equations -- 3 Affinely regular n-gons -- 4 Three extreme cases for the Boolean algebra of cyclic n-gonal classes -- 5 Real components of an n-gon -- Appendices -- 1 Lattices -- 2 Cyclotomic polynomials -- List of symbols and notations -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- V -- W -- X -- Y -- Z. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Polygons. | |
| 650 | 0 | |a Set theory. | |
| 650 | 6 | |a Polygones. | |
| 650 | 6 | |a Théorie des ensembles. | |
| 650 | 7 | |a polygons. |2 aat | |
| 650 | 7 | |a Polygons |2 fast | |
| 650 | 7 | |a Set theory |2 fast | |
| 700 | 1 | |a Schmidt, Eckart. | |
| 700 | 1 | |a Garner, Cyril W. L. | |
| 758 | |i has work: |a N-gons (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGmcfpGdXWQmrXdG7M9BCP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Bachmann, Friedrich. |t N-gons. |d Toronto : University of Toronto Press, ©1975 |z 9781442651548 |
| 830 | 0 | |a Heritage. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=4669449 |z Texto completo |
| 880 | 0 | |6 505-01/(S |a Cover -- Contents -- Author's preface -- Translator's preface -- Summary of contents -- Introduction -- PART I: Cyclic classes and cyclic mappings -- 1 Cyclic classes of n-gons -- 1 n-gons, vector space of n-gons -- 2 Cyclic classes -- 3 The centre-of-gravity n-gon. The zero isobaric class -- 4 Two types of cyclic classes -- 5 Periodic classes -- 6 Degree of freedom of a cyclic class -- 7 Dimension of an n-gon -- 8 Examples of cyclic classes -- 2 Cyclic mappings of n-gons -- 1 Cyclic mappings -- 2 The algebra of cyclic mappings -- 3 Coefficient sum of a cyclic mapping -- 4 Projections -- 5 Examples -- 6 A cyclic quasi-projection -- 7 Isobaric cyclic projections for n = 4 -- 8 Cyclic matrices -- 3 Isobaric cyclic mappings -- 1 σ-kernel -- 2 Two types of cyclic classes -- 3 Remarks concerning isobaric cyclic mappings -- Notes concerning the addition of n-gons -- 1 Addition of n-gons -- 2 Displacement of addition in an abelian group -- 3 Addition of isobaric n-gons with respect to the centre of gravity -- 4 Averaging mappings -- 1 Isobarically splitting n-gons -- 2 Omitting averaging projections -- 3 The complementary projections -- 4 Consecutive averaging projections -- PART II: The main theorem -- 5 Idempotent elements and Boolean algebras -- 1 Idempotent elements of a ring -- 2 Finitely generated Boolean algebras -- 3 Idempotent endomorphisms of an abelian group: Im-transfer -- 4 The Boolean algebra of cyclic projections -- 5 Examples of Im-transfer -- 6 The main theorem about cyclic classes -- 1 Congruences in principal ideal domains -- 2 Main theorems about cyclic mappings and cyclic classes -- 3 The prime factors of xⁿ -- 1 and the atomic cyclic classes -- PART III: Boolean algebras of n-gonal theory -- 7 Idempotent-transfer. Residue class rings of principal ideal domains -- 1 R-modules -- 2 Idempotent-transfer. | |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL4669449 | ||
| 994 | |a 92 |b IZTAP | ||