Mathematics across the Iron Curtain: a history of the algebraic theory of semigroups
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2014
|
| Schriftenreihe: | History of mathematics
41 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027484065&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 441 S. 26 cm |
| ISBN: | 9781470414931 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematics across the Iron Curtain |b a history of the algebraic theory of semigroups |c Christopher Hollings |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2014 | |
| 300 | |a XI, 441 S. |c 26 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a History of mathematics |v 41 | |
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Datensatz im Suchindex
| _version_ | 1819361956270702592 |
|---|---|
| adam_text | Contents
Preface
vii
Languages
ix
Acknowledgements x
Chapter
1.
Algebra at the Beginning of the Twentieth Century
1
1.1.
A changing discipline
1
1.2.
The term semigroup
3
1.3.
An overview of the development of semigroup theory
7
Chapter
2.
Communication between East and West
11
2.1.
Communication down through the decades
14
2.2.
Access to publications
29
Chapter
3.
Anton Kazimirovich Sushkevich
45
3.1.
Biography
47
3.2.
The theory of operations as the general theory of groups
54
3.3.
Generalised groups
58
3.4.
Sushkevich s impact
73
Chapter
4.
Unique Factorisation in Semigroups
77
4.1.
Postulational analysis
81
4.2.
E. T.
Bell and the arithmetisation of algebra
83
4.3.
Morgan Ward and the foundations of general arithmetic
88
4.4.
Alfred H. Clifford
91
4.5.
Arithmetic of ova
93
4.6.
Subsequent developments
103
Chapter
5.
Embedding Semigroups in Groups
107
5.1.
The theorems of Steinitz and Ore 111
5.2.
Embedding according to Sushkevich
116
5.3.
Further sufficient conditions
122
5.4.
Maltsev s immersibility conditions
124
5.5.
Other embedding problems
133
Chapter
6.
The
Rees
Theorem
135
6.1.
Completely (O-)simple semigroups
137
6.2.
Brandt groupoids
140
6.3.
Sushkevich s
Kerngruppen 145
6.4.
Clifford s multiple groups
149
6.5.
The
Rees
Theorem
151
6.6.
Unions of groups and semigroups
156
vi
CONTENTS
Chapter
7.
The French School of
Demi-groupes
161
7.1.
Paul Dubreil and Marie-Louise Dubreil-Jacotin
164
7.2.
Equivalence relations
166
7.3.
Principal equivalences and related concepts
171
7.4.
Subsequent work
177
Chapter
8.
The Expansion of the Theory in the
1940s
and
1950s 183
8.1.
The growth of national schools
184
8.2.
The Slovak school
186
8.3.
The American school
192
8.4.
The Japanese school
201
8.5.
The Hungarian school
206
8.6.
British authors
208
Chapter
9.
The Post-Sushkevich Soviet School
217
9.1.
Evgenii Sergeevich Lyapin
220
9.2.
Lyapin s mathematical work
225
9.3.
Lazar
Matveevich Gluskin
238
9.4.
Gluskin s mathematical work
239
9.5.
Other authors
246
Chapter
10.
The Development of Inverse Semigroups
249
10.1.
A little theory
251
10.2.
Pseudogroups and conceptual difficulties
252
10.3.
Viktor Vladimirovich Wagner
258
10.4.
Wagner and generalised groups
259
10.5.
Gordon B. Preston
268
10.6.
Preston and inverse semigroups
269
Chapter
11.
Matrix Representations of Semigroups
277
11.1.
Sushkevich on matrix semigroups
281
11.2.
Clifford on matrix semigroups
285
11.3.
W. Douglas Munn
289
11.4.
The work of W. D. Munn
291
11.5.
The work of J. S. Ponizovskii
298
Chapter
12.
Books, Seminars, Conferences, and Journals
303
12.1.
Monographs
305
12.2.
Seminars on semigroups
323
12.3.
Czechoslovakia,
1968,
and Semigroup Forum
326
Appendix. Basic Theory
333
Notes
337
Bibliography
373
Name Index
429
Subject Index
433
|
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| discipline | Mathematik |
| era | Geschichte 1904-1970 gnd |
| era_facet | Geschichte 1904-1970 |
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| id | DE-604.BV042042838 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:00:47Z |
| institution | BVB |
| isbn | 9781470414931 |
| language | English |
| lccn | 2014008281 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027484065 |
| oclc_num | 889991621 |
| open_access_boolean | |
| owner | DE-12 DE-19 DE-BY-UBM DE-210 DE-11 DE-188 |
| owner_facet | DE-12 DE-19 DE-BY-UBM DE-210 DE-11 DE-188 |
| physical | XI, 441 S. 26 cm |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | History of mathematics |
| series2 | History of mathematics |
| spellingShingle | Hollings, Christopher 1982- Mathematics across the Iron Curtain a history of the algebraic theory of semigroups History of mathematics Ost-West-Konflikt (DE-588)4075770-5 gnd Mathematik (DE-588)4037944-9 gnd Halbgruppentheorie (DE-588)4288418-4 gnd Wissenschaftsentwicklung (DE-588)4079355-2 gnd |
| subject_GND | (DE-588)4075770-5 (DE-588)4037944-9 (DE-588)4288418-4 (DE-588)4079355-2 |
| title | Mathematics across the Iron Curtain a history of the algebraic theory of semigroups |
| title_auth | Mathematics across the Iron Curtain a history of the algebraic theory of semigroups |
| title_exact_search | Mathematics across the Iron Curtain a history of the algebraic theory of semigroups |
| title_full | Mathematics across the Iron Curtain a history of the algebraic theory of semigroups Christopher Hollings |
| title_fullStr | Mathematics across the Iron Curtain a history of the algebraic theory of semigroups Christopher Hollings |
| title_full_unstemmed | Mathematics across the Iron Curtain a history of the algebraic theory of semigroups Christopher Hollings |
| title_short | Mathematics across the Iron Curtain |
| title_sort | mathematics across the iron curtain a history of the algebraic theory of semigroups |
| title_sub | a history of the algebraic theory of semigroups |
| topic | Ost-West-Konflikt (DE-588)4075770-5 gnd Mathematik (DE-588)4037944-9 gnd Halbgruppentheorie (DE-588)4288418-4 gnd Wissenschaftsentwicklung (DE-588)4079355-2 gnd |
| topic_facet | Ost-West-Konflikt Mathematik Halbgruppentheorie Wissenschaftsentwicklung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027484065&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001327576 |
| work_keys_str_mv | AT hollingschristopher mathematicsacrosstheironcurtainahistoryofthealgebraictheoryofsemigroups |