Infinite algebraic extensions of finite fields:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
1989
|
| Series: | Contemporary Mathematics
95 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 104 Seiten |
| ISBN: | 0821851012 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV002620759 | ||
| 003 | DE-604 | ||
| 005 | 20200507 | ||
| 007 | t | ||
| 008 | 900430s1989 |||| 00||| engod | ||
| 020 | |a 0821851012 |9 0-8218-5101-2 | ||
| 035 | |a (OCoLC)19815433 | ||
| 035 | |a (DE-599)BVBBV002620759 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-384 |a DE-739 |a DE-355 |a DE-29T |a DE-19 |a DE-188 |a DE-83 | ||
| 050 | 0 | |a QA247 | |
| 082 | 0 | |a 512/.75 |2 20 | |
| 084 | |a SI 805 |0 (DE-625)143193: |2 rvk | ||
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 084 | |a 12F05 |2 msc | ||
| 084 | |a 12C05 |2 msc | ||
| 100 | 1 | |a Brawley, Joel V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Infinite algebraic extensions of finite fields |c Joel V. Brawley and George E. Schnibben |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1989 | |
| 300 | |a XV, 104 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Contemporary Mathematics |v 95 | |
| 650 | 4 | |a Corps algébriques | |
| 650 | 7 | |a Corps algébriques |2 ram | |
| 650 | 7 | |a Corps fini |2 Jussieu | |
| 650 | 7 | |a Extension algébrique |2 Jussieu | |
| 650 | 4 | |a Extensions de corps (Mathématiques) | |
| 650 | 7 | |a Extensions de corps (Mathématiques) |2 ram | |
| 650 | 7 | |a Polynôme |2 Jussieu | |
| 650 | 4 | |a Algebraic fields | |
| 650 | 4 | |a Field extensions (Mathematics) | |
| 650 | 0 | 7 | |a Körpererweiterung |0 (DE-588)4164435-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Erweiterung |0 (DE-588)4128080-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraischer Körper |0 (DE-588)4141852-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Galois-Feld |0 (DE-588)4155896-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Galois-Feld |0 (DE-588)4155896-0 |D s |
| 689 | 0 | 1 | |a Körpererweiterung |0 (DE-588)4164435-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Körpererweiterung |0 (DE-588)4164435-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Algebraischer Körper |0 (DE-588)4141852-9 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Algebraischer Körper |0 (DE-588)4141852-9 |D s |
| 689 | 3 | 1 | |a Erweiterung |0 (DE-588)4128080-5 |D s |
| 689 | 3 | |5 DE-604 | |
| 700 | 1 | |a Schnibben, George E. |e Verfasser |4 aut | |
| 830 | 0 | |a Contemporary Mathematics |v 95 |w (DE-604)BV000003365 |9 95 | |
| 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=001684176&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001684176 | ||
Record in the Search Index
| _version_ | 1804117004999720960 |
|---|---|
| adam_text | CONTENTS
Page
PREFACE xiii
CHAPTER 1. A SURVEY OF SOME FINITE FIELD THEORY
1.1. Introduction 1
1.2. Finite Fields 1
1.3. Finite Extensions and Irreducible Polynomials 6
1.4. Polynomial Representation of Functions on a Finite Field 11
CHAPTER 2. ALGEBRAIC EXTENSIONS OF FINITE FIELDS
2.1. Introduction 21
2.2. The Algebraic Closure of a Finite Field 22
2.3. Subfields of the Algebraic Closure 23
2.4. Automorphisms of Subfields of the Algebraic Closure 31
CHAPTER 3. ITERATED PRESENTATIONS AND EXPLICIT
BASES
3.1. Introduction 37
3.2. Definitions of Iterated Presentation and Explicit Basis 39
3.3. Iterated Presentations of the Fields GF(pp°°) 44
3.4. Iterated Presentations of the Fields GFCq^ 1^00), p^q=l 49
3.5. Several Additional Iterated Presentations 57
CHAPTER 4. POLYNOMIALS AND POLYNOMIAL FUNCTIONS
4.1. Introduction 61
4.2. Irreducible Polynomials over GF(qN) 62
4.3. Permutation Monomials on GF(qN) 68
4.4. Permutation q Polynomials on GF(qN) 73
4.5. Dickson Polynomials over GF(qN) 79
4.6. Representation of Functions of GF(qN) 81
4.7. Representation of Linear Transformations on GF(qN) 84
xi
xii CONTENTS
CHAPTER 5. TWO APPLICATIONS
5.1. Introduction 87
5.2. Orthogonal Latin Squares 88
5.3. Permutation Polynomials on the Matrices over GF(qN) 92
BIBLIOGRAPHY 101
|
| any_adam_object | 1 |
| author | Brawley, Joel V. Schnibben, George E. |
| author_facet | Brawley, Joel V. Schnibben, George E. |
| author_role | aut aut |
| author_sort | Brawley, Joel V. |
| author_variant | j v b jv jvb g e s ge ges |
| building | Verbundindex |
| bvnumber | BV002620759 |
| callnumber-first | Q - Science |
| callnumber-label | QA247 |
| callnumber-raw | QA247 |
| callnumber-search | QA247 |
| callnumber-sort | QA 3247 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 805 SK 230 |
| ctrlnum | (OCoLC)19815433 (DE-599)BVBBV002620759 |
| dewey-full | 512/.75 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.75 |
| dewey-search | 512/.75 |
| dewey-sort | 3512 275 |
| 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>02488nam a2200649 cb4500</leader><controlfield tag="001">BV002620759</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200507 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">900430s1989 |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821851012</subfield><subfield code="9">0-8218-5101-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)19815433</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002620759</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-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA247</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.75</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 805</subfield><subfield code="0">(DE-625)143193:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 230</subfield><subfield code="0">(DE-625)143225:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">12F05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">12C05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Brawley, Joel V.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Infinite algebraic extensions of finite fields</subfield><subfield code="c">Joel V. Brawley and George E. Schnibben</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 104 Seiten</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">Contemporary Mathematics</subfield><subfield code="v">95</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Corps algébriques</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Corps algébriques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Corps fini</subfield><subfield code="2">Jussieu</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Extension algébrique</subfield><subfield code="2">Jussieu</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Extensions de corps (Mathématiques)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Extensions de corps (Mathématiques)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Polynôme</subfield><subfield code="2">Jussieu</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic fields</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Field extensions (Mathematics)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Körpererweiterung</subfield><subfield code="0">(DE-588)4164435-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Erweiterung</subfield><subfield code="0">(DE-588)4128080-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraischer Körper</subfield><subfield code="0">(DE-588)4141852-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Galois-Feld</subfield><subfield code="0">(DE-588)4155896-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Galois-Feld</subfield><subfield code="0">(DE-588)4155896-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Körpererweiterung</subfield><subfield code="0">(DE-588)4164435-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Körpererweiterung</subfield><subfield code="0">(DE-588)4164435-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Algebraischer Körper</subfield><subfield code="0">(DE-588)4141852-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Algebraischer Körper</subfield><subfield code="0">(DE-588)4141852-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2="1"><subfield code="a">Erweiterung</subfield><subfield code="0">(DE-588)4128080-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schnibben, George E.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Contemporary Mathematics</subfield><subfield code="v">95</subfield><subfield code="w">(DE-604)BV000003365</subfield><subfield code="9">95</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=001684176&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:BVB01-001684176</subfield></datafield></record></collection> |
| id | DE-604.BV002620759 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:47:31Z |
| institution | BVB |
| isbn | 0821851012 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001684176 |
| oclc_num | 19815433 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-739 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-188 DE-83 |
| owner_facet | DE-12 DE-384 DE-739 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-188 DE-83 |
| physical | XV, 104 Seiten |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Contemporary Mathematics |
| series2 | Contemporary Mathematics |
| spelling | Brawley, Joel V. Verfasser aut Infinite algebraic extensions of finite fields Joel V. Brawley and George E. Schnibben Providence, RI American Mathematical Society 1989 XV, 104 Seiten txt rdacontent n rdamedia nc rdacarrier Contemporary Mathematics 95 Corps algébriques Corps algébriques ram Corps fini Jussieu Extension algébrique Jussieu Extensions de corps (Mathématiques) Extensions de corps (Mathématiques) ram Polynôme Jussieu Algebraic fields Field extensions (Mathematics) Körpererweiterung (DE-588)4164435-9 gnd rswk-swf Erweiterung (DE-588)4128080-5 gnd rswk-swf Algebraischer Körper (DE-588)4141852-9 gnd rswk-swf Galois-Feld (DE-588)4155896-0 gnd rswk-swf Galois-Feld (DE-588)4155896-0 s Körpererweiterung (DE-588)4164435-9 s DE-604 Algebraischer Körper (DE-588)4141852-9 s Erweiterung (DE-588)4128080-5 s Schnibben, George E. Verfasser aut Contemporary Mathematics 95 (DE-604)BV000003365 95 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001684176&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brawley, Joel V. Schnibben, George E. Infinite algebraic extensions of finite fields Contemporary Mathematics Corps algébriques Corps algébriques ram Corps fini Jussieu Extension algébrique Jussieu Extensions de corps (Mathématiques) Extensions de corps (Mathématiques) ram Polynôme Jussieu Algebraic fields Field extensions (Mathematics) Körpererweiterung (DE-588)4164435-9 gnd Erweiterung (DE-588)4128080-5 gnd Algebraischer Körper (DE-588)4141852-9 gnd Galois-Feld (DE-588)4155896-0 gnd |
| subject_GND | (DE-588)4164435-9 (DE-588)4128080-5 (DE-588)4141852-9 (DE-588)4155896-0 |
| title | Infinite algebraic extensions of finite fields |
| title_auth | Infinite algebraic extensions of finite fields |
| title_exact_search | Infinite algebraic extensions of finite fields |
| title_full | Infinite algebraic extensions of finite fields Joel V. Brawley and George E. Schnibben |
| title_fullStr | Infinite algebraic extensions of finite fields Joel V. Brawley and George E. Schnibben |
| title_full_unstemmed | Infinite algebraic extensions of finite fields Joel V. Brawley and George E. Schnibben |
| title_short | Infinite algebraic extensions of finite fields |
| title_sort | infinite algebraic extensions of finite fields |
| topic | Corps algébriques Corps algébriques ram Corps fini Jussieu Extension algébrique Jussieu Extensions de corps (Mathématiques) Extensions de corps (Mathématiques) ram Polynôme Jussieu Algebraic fields Field extensions (Mathematics) Körpererweiterung (DE-588)4164435-9 gnd Erweiterung (DE-588)4128080-5 gnd Algebraischer Körper (DE-588)4141852-9 gnd Galois-Feld (DE-588)4155896-0 gnd |
| topic_facet | Corps algébriques Corps fini Extension algébrique Extensions de corps (Mathématiques) Polynôme Algebraic fields Field extensions (Mathematics) Körpererweiterung Erweiterung Algebraischer Körper Galois-Feld |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001684176&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003365 |
| work_keys_str_mv | AT brawleyjoelv infinitealgebraicextensionsoffinitefields AT schnibbengeorgee infinitealgebraicextensionsoffinitefields |