Antimorphic action: categories of algebraic structures with involutions or anti-endomorphisms
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Heldermann
1986
|
| Series: | Research and exposition in mathematics
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 189 S. |
| ISBN: | 3885382121 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV000670893 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 871202s1986 |||| 00||| eng d | ||
| 020 | |a 3885382121 |9 3-88538-212-1 | ||
| 035 | |a (OCoLC)16114423 | ||
| 035 | |a (DE-599)BVBBV000670893 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-739 |a DE-29T |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA155.5 | |
| 082 | 0 | |a 511.3/24 |2 19 | |
| 084 | |a SK 320 |0 (DE-625)143231: |2 rvk | ||
| 100 | 1 | |a Cornish, William H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Antimorphic action |b categories of algebraic structures with involutions or anti-endomorphisms |c W. H. Cornish |
| 264 | 1 | |a Berlin |b Heldermann |c 1986 | |
| 300 | |a XIX, 189 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Research and exposition in mathematics |v 12 | |
| 650 | 7 | |a Catégories (mathématiques) |2 ram | |
| 650 | 7 | |a Involution (Mathématiques) |2 ram | |
| 650 | 7 | |a Logique algébrique |2 ram | |
| 650 | 7 | |a Treillis, Théorie des |2 ram | |
| 650 | 4 | |a Algebraic logic | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Involutes (Mathematics) | |
| 650 | 4 | |a Lattice theory | |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kategorientheorie |0 (DE-588)4120552-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kategorientheorie |0 (DE-588)4120552-2 |D s |
| 689 | 0 | 1 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Research and exposition in mathematics |v 12 |w (DE-604)BV000017533 |9 12 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000418669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-000418669 | ||
Record in the Search Index
| _version_ | 1804115119331868672 |
|---|---|
| adam_text | vi
Table of Contents,
j^. Abstract Expansions 1
1.1_ An expansion by antimorphisms of a category 1
1.2 Conjugator between expansions 2
1.3 An expansion with an involution 2
1.4 The trivial expansion 3
1.5 Expansion with the anti identity as an involution 3
1.6. The separation of an expansion 4
1.7 The pairwise expansion 5
1.8 The induced expansion of a full self conjugate subcategory 6
l_.jt The expansion of Cat 7
1.10 The opposite of an expansion; contravariant conjugators .. 9
i. Concrete Expansions 11
2.1 ^ concrete expansions and expandable J^ concrete categories 15
2.3 Induced K concrete expansions 15
2.4 Concrete categories, concrete expansions and expandable
concrete categories 16
3_. Examples 18
3.1 Groupoids, semigroups, loops 18
3.2 Bigroupoids; latttices, skew lattices; equational
quasigroups; Kimura s isomorphism 21
3_j_3_ Non associative rings and algebras 27
3.4 Vector spaces and algebras over the complex numbers 31
3.5 A Set concrete expansion of rings, which is not a
concrete expansion 32
3_.6 Directed graphs, posets, ordered topological spaces 33
vii
3.7 Some expansions from General Topology 36
3.8 Jordan pairs, alternative pairs, and associative pairs .... 39
3.9 Superalgebras; graded skew symmetry; Lie superalgebras .... 42
4. The Involution Theorem 48
4.1 Involution or reflection for a functor 48
4.2 The involution theorem 48
4.3 Its principal corollary 50
4.4 The involution on free algebras 51
4.7 Examples of 4.2 52
4.8. Examples of 4.3 54
iLit Examples of 4.4 59
4.10 Examples of 4.6 61
4.11 De Morgan algebras 64
iL. ± Monoids and their Actions 65
5.1 ± monoid 65
5.11 Action of a ± monoid 68
S..12 The category M K 09
5.14. The category of ^ objects with an involution 70
5.15 Associative pairs with an involution 71
5.16 The action on a variety 71
5.17 The action on a category with an involution 76
6=. Induced Equivalences and Dualities for M i 79
6_.J. The induced equivalence and duality theorems 79
6.2 Spec M and Tpdc M 82
6.3. The dual of BJT and expansions of related categories 83
6.4 Subvarieties of M M and their duals 88
viii
£. The Creation of Limits and Colimits for, M )C 98
7.7 Creation of limits 101
7.12 Creation of colimits 102
7.14 De Morgan algebras 103
7.15 Coproducts of semigroups with an involution and inverse
semigroups 104
7.16 A representation of the coproducts of two algebras in M gll 104
7.17 Coreflective subvarieties of M X^ 107
7.18 Liftable properties of the variety }C Ill
JL. Righti and Left Ad joints. 114
8.8 The right adjoints of | |:M ^—»¦£ 121
8.16 The left adjoint of | | :M £—?X, 124
8.17 Free extensions 124
8.18. Free algebras 130
.8.19 Concerning the right adj oint 135
jj.20 Cogenerators and residual smallness 137
JL,_21_ The congruence extension property 139
8^22 Amalgamation, transferable injections, and injective
completeness , 141
£. Congruences and M X Subdirectly IrreduciMes. 147
9jJl_ Principal M Xrcongruences 147
g_._2_ The left action of M on M X Con(A), when M is a group .... 151
9.3 Discriminator varieties 156
g^j. G(A) as a subdirectly irreducible; quasiprimality 157
g.5 A structure theorem; amalgamation; lattice of
subvarieties 162
g.6 The dual form for congruences and subdirectly irreducible
M gjl algebras 165
9.7 The nature of the cogenerator, G(£), of M BD^ 168
ix
References 172
Additional References 179
Notation 181
JndejL 183
|
| any_adam_object | 1 |
| author | Cornish, William H. |
| author_facet | Cornish, William H. |
| author_role | aut |
| author_sort | Cornish, William H. |
| author_variant | w h c wh whc |
| building | Verbundindex |
| bvnumber | BV000670893 |
| callnumber-first | Q - Science |
| callnumber-label | QA155 |
| callnumber-raw | QA155.5 |
| callnumber-search | QA155.5 |
| callnumber-sort | QA 3155.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 320 |
| ctrlnum | (OCoLC)16114423 (DE-599)BVBBV000670893 |
| dewey-full | 511.3/24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/24 |
| dewey-search | 511.3/24 |
| dewey-sort | 3511.3 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01842nam a2200481 cb4500</leader><controlfield tag="001">BV000670893</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">871202s1986 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3885382121</subfield><subfield code="9">3-88538-212-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)16114423</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV000670893</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA155.5</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3/24</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 320</subfield><subfield code="0">(DE-625)143231:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cornish, William H.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Antimorphic action</subfield><subfield code="b">categories of algebraic structures with involutions or anti-endomorphisms</subfield><subfield code="c">W. H. Cornish</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin</subfield><subfield code="b">Heldermann</subfield><subfield code="c">1986</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIX, 189 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Research and exposition in mathematics</subfield><subfield code="v">12</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Catégories (mathématiques)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Involution (Mathématiques)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Logique algébrique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Treillis, Théorie des</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic logic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Categories (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Involutes (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lattice theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kategorientheorie</subfield><subfield code="0">(DE-588)4120552-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kategorientheorie</subfield><subfield code="0">(DE-588)4120552-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Research and exposition in mathematics</subfield><subfield code="v">12</subfield><subfield code="w">(DE-604)BV000017533</subfield><subfield code="9">12</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000418669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-000418669</subfield></datafield></record></collection> |
| id | DE-604.BV000670893 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:33Z |
| institution | BVB |
| isbn | 3885382121 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000418669 |
| oclc_num | 16114423 |
| open_access_boolean | |
| owner | DE-12 DE-739 DE-29T DE-11 DE-188 |
| owner_facet | DE-12 DE-739 DE-29T DE-11 DE-188 |
| physical | XIX, 189 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Heldermann |
| record_format | marc |
| series | Research and exposition in mathematics |
| series2 | Research and exposition in mathematics |
| spelling | Cornish, William H. Verfasser aut Antimorphic action categories of algebraic structures with involutions or anti-endomorphisms W. H. Cornish Berlin Heldermann 1986 XIX, 189 S. txt rdacontent n rdamedia nc rdacarrier Research and exposition in mathematics 12 Catégories (mathématiques) ram Involution (Mathématiques) ram Logique algébrique ram Treillis, Théorie des ram Algebraic logic Categories (Mathematics) Involutes (Mathematics) Lattice theory Algebra (DE-588)4001156-2 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s Algebra (DE-588)4001156-2 s DE-604 Research and exposition in mathematics 12 (DE-604)BV000017533 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000418669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cornish, William H. Antimorphic action categories of algebraic structures with involutions or anti-endomorphisms Research and exposition in mathematics Catégories (mathématiques) ram Involution (Mathématiques) ram Logique algébrique ram Treillis, Théorie des ram Algebraic logic Categories (Mathematics) Involutes (Mathematics) Lattice theory Algebra (DE-588)4001156-2 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4120552-2 |
| title | Antimorphic action categories of algebraic structures with involutions or anti-endomorphisms |
| title_auth | Antimorphic action categories of algebraic structures with involutions or anti-endomorphisms |
| title_exact_search | Antimorphic action categories of algebraic structures with involutions or anti-endomorphisms |
| title_full | Antimorphic action categories of algebraic structures with involutions or anti-endomorphisms W. H. Cornish |
| title_fullStr | Antimorphic action categories of algebraic structures with involutions or anti-endomorphisms W. H. Cornish |
| title_full_unstemmed | Antimorphic action categories of algebraic structures with involutions or anti-endomorphisms W. H. Cornish |
| title_short | Antimorphic action |
| title_sort | antimorphic action categories of algebraic structures with involutions or anti endomorphisms |
| title_sub | categories of algebraic structures with involutions or anti-endomorphisms |
| topic | Catégories (mathématiques) ram Involution (Mathématiques) ram Logique algébrique ram Treillis, Théorie des ram Algebraic logic Categories (Mathematics) Involutes (Mathematics) Lattice theory Algebra (DE-588)4001156-2 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Catégories (mathématiques) Involution (Mathématiques) Logique algébrique Treillis, Théorie des Algebraic logic Categories (Mathematics) Involutes (Mathematics) Lattice theory Algebra Kategorientheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000418669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000017533 |
| work_keys_str_mv | AT cornishwilliamh antimorphicactioncategoriesofalgebraicstructureswithinvolutionsorantiendomorphisms |