Categories of algebraic systems: vector and projective spaces, semigroups, rings and lattices
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1976
|
| Series: | Lecture notes in mathematics
553 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 217 S. |
| ISBN: | 354007998X 038707998X |
Staff View
MARC
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| 245 | 1 | 0 | |a Categories of algebraic systems |b vector and projective spaces, semigroups, rings and lattices |c Mario Petrich |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1976 | |
| 300 | |a VIII, 217 S. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 553 | |
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Record in the Search Index
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|---|---|
| adam_text | TABLE OF CONTENTS
INTRODUCTION 1
1 * Motivation 1
2* Summary 5
3* Preliminaries on categories 7
I. VECTOR SPACES 11
§1 Pairs of dual vector Spaces and regulär linear
Systems
(Categories n,T; Functor S») 12
§2 Regulär linear Systems and weakly topologized
vector spaces
(Categories T,H; Functor 83) 16
II. SEMIGROUPS 19
§3 Dense extension of primitive regulär semigroups
(Categories I.I^M.M^ 20
§4 Pairs of dual vector Spaces and completely 0-simple
semigroups
(Categories Ii^.E^; Functors £., i = 3,5) 26
§5 Primitive regulär semigroups and their maximal
dense extensions
(Categories 1^,1^, i = 3,5;
Functors ^,5^,s.s^ i = 1-5) 31
III. RINGS 39
§6 Semisimple atomic rings and their maximal essential
extensions
VI
(Categories P,Pi,M,Mi; Functors 3i0i.5-.Ci. i = 1-5). 40
§7 Maximal essential extensions of rings and maximal
dense extensions of semigroups
(Functors $±, i = 2-5) 47
IV. LATTICES 50
§8 Subprojective lattices
(Categories A,Ai, i = 1-5) 51
§9 Semisimple atomic rings and subprojective lattices
(Functors «,ft±, i = 1-5) 56
V. PROJECTIVE SPACES 63
§10 Generalities
(Category 1) 64
§11 Subprojective lattices and pairs of dual protective spaces
(Category A ; Functors tt.Ol) 73
§12 Properties of functors D and 9l
(Categories 1.; Functors E.. ,2i., i = 4,5) 83
§13 Regular linear systems and pairs of dual protective
spaces
(Categories i ^,! ,-,T,-; Functor $,-) 92
VI. THE LOOP 99
§14 Commutativity of the loop
(Functor e^) 99
§15 The equivalence of P. and A. for i = 4,5
(Functors R^.R^) 106
VII
VII. ANTIAUTOMORPHISMS 114
§16 Antiautomorphisms of semigroups
(Categories Ii,Mi; Functors S^.S^ i = 6-8) 116
§17 Antiautomorphisms of rings
(Categories P1,Ni,M1; Functors Q^S^^, i = 6-8) 122
§18 Antiautomorphisms of lattices
(Categories Pi Ai; Functors Ri, i = 6-8) 125
§19 Correlations and subprojective lattices
(Categories I , fA,! Functors ir^.Dl^, i = 6-8) 131
§20 Scalar products and correlations
(Categories ^,1^; Functors S^, i = 6-8) 140
§21 Scalar products and antiautomorphisms of semigroups
(Categories H±,I.±; Functors £i, i = 6-8) 151
§22 Commutativity of the loop
(Functors e±, i = 6-8) 158
§23 The equivalence of P, and A. for i = 6-8
(Functors J^, i = 6-8) 161
VIII. SPECIAL CASES 168
§24 Vector spaces, semigroups and rings
(Categories II^E^.M^P^I^;
Functors t±,%i,tti, ^.ag.^. i = 9,10) 169
§25 Rings and lattices
(Categories P^^; Functors j^, i = 9,10) 175
§26 Lattices, vector and protective spaces
(Categories A^I^.I^; Functors iBl.^,9^,»i, i = 9,10) 182
VIII
BIBLIOGRAPHY 188
DIAGRAMS 199
LIST OF CATEGORIES 203
LIST OF FUNCTORS 206
SPECIAL SYMBOLS 208
INDEX 212
|
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| dewey-full | 512 510/.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512 510/.8 |
| dewey-search | 512 510/.8 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV001972225 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:38:09Z |
| institution | BVB |
| isbn | 354007998X 038707998X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001286307 |
| oclc_num | 264210314 |
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| physical | VIII, 217 S. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Petrich, Mario Verfasser aut Categories of algebraic systems vector and projective spaces, semigroups, rings and lattices Mario Petrich Berlin [u.a.] Springer 1976 VIII, 217 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 553 Algèbre abstraite Catégories (Mathématiques) Algebra, Abstract Categories (Mathematics) Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 s Algebraische Struktur (DE-588)4001166-5 s DE-604 Lecture notes in mathematics 553 (DE-604)BV000676446 553 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001286307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petrich, Mario Categories of algebraic systems vector and projective spaces, semigroups, rings and lattices Lecture notes in mathematics Algèbre abstraite Catégories (Mathématiques) Algebra, Abstract Categories (Mathematics) Algebraische Struktur (DE-588)4001166-5 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4001166-5 (DE-588)4129930-9 |
| title | Categories of algebraic systems vector and projective spaces, semigroups, rings and lattices |
| title_auth | Categories of algebraic systems vector and projective spaces, semigroups, rings and lattices |
| title_exact_search | Categories of algebraic systems vector and projective spaces, semigroups, rings and lattices |
| title_full | Categories of algebraic systems vector and projective spaces, semigroups, rings and lattices Mario Petrich |
| title_fullStr | Categories of algebraic systems vector and projective spaces, semigroups, rings and lattices Mario Petrich |
| title_full_unstemmed | Categories of algebraic systems vector and projective spaces, semigroups, rings and lattices Mario Petrich |
| title_short | Categories of algebraic systems |
| title_sort | categories of algebraic systems vector and projective spaces semigroups rings and lattices |
| title_sub | vector and projective spaces, semigroups, rings and lattices |
| topic | Algèbre abstraite Catégories (Mathématiques) Algebra, Abstract Categories (Mathematics) Algebraische Struktur (DE-588)4001166-5 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Algèbre abstraite Catégories (Mathématiques) Algebra, Abstract Categories (Mathematics) Algebraische Struktur Kategorie Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001286307&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT petrichmario categoriesofalgebraicsystemsvectorandprojectivespacessemigroupsringsandlattices |