Finite commutative rings and their applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston
Kluwer Academic Publishers
2002
|
| Schriftenreihe: | The Kluwer international series in engineering and computer science
680 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | x, 176 p. |
| ISBN: | 140207039X |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | FINITE COMMUTATIVE RINGS AND THEIR APPLICATIONS GILBERTO BINI UNIVERSITY
OF MICHIGAN U.S.A. FLAMINIO FLAMINI UNIVERSITA DEGLI STUDI ROMA TRE
ITALY KLUWER ACADEMIC PUBLISHERS BOSTON / DORDRECHT / LONDON CONTENTS
FOREWORD VII PREFACE IX FUNDAMENTAL NOTIONS IN RING THEORY 1 1.1 BASIC
DEFINITIONS 1 1.2 PRIME AND MAXIMAL IDEALS 3 1.3 EUCLIDEAN DOMAINS,
P.I.D. S AND U.F.D. S 9 1.4 FACTORIZATION IN Z P N[X] 20 FINITE FIELD
STRUCTURE 29 2.1 BASIC PROPERTIES 29 2.2 CHARACTERIZATION OF FINITE
FIELDS 31 2.3 GALOIS FIELD AUTOMORPHISMS 34 FINITE COMMUTATIVE RINGS.
REGULAR POLY- NOMIALS 39 3.1 FINITE COMMUTATIVE RING STRUCTURE 39 3.2
REGULAR POLYNOMIALS IN THE RING R[X) 47 3.3 I?-ALGEBRA AUTOMORPHISMS OF
R[X] 54 3.4 FACTORIZATION IN R[X] 56 SEPARABLE EXTENSIONS OF FINITE
FIELDS AND FINITE RINGS 61 4.1 SEPARABLE FIELD EXTENSIONS 61 4.2
EXTENSIONS OF RINGS 65 4.3 * SEPARABLE EXTENSIONS OF FINITE COMMUTATIVE
LOCAL RINGS . . 67 GALOIS THEORY FOR LOCAL RINGS 71 5.1 BASIC FACTS 71
VI CONTENTS 5.2 EXAMPLES. SPLITTING RINGS 75 6 GALOIS AND QUASI-GALOIS
RINGS: STRUCTURE AND PROPERTIES 81 6.1 CLASSICAL CONSTRUCTIONS 82 6.2
GALOIS RING PROPERTIES 92 6.3 STRUCTURE THEOREMS FOR FINITE COMMUTATIVE
LOCAL RINGS . . 105 6.4 ANOTHER CLASS OF FINITE COMMUTATIVE LOCAL RINGS:
QUASI- GALOIS RINGS 107 7 BASIC NOTIONS ON CODES OVER FINITE FIELDS 121
7.1 BASIC PROPERTIES 121 7.2 SOME FAMILIES OF G-ARY CODES 122 7.2.1
LINEAR CODES 122 7.2.2 HAMMING CODES 123 7.2.3 CYCLIC CODES 124 7.2.4
REED-MULLER CODES 129 7.3 DUALITY BETWEEN CODES 130 7.4 SOME FAMILIES OF
NONLINEAR G-ARY CODES 134 7.4.1 BINARY KERDOCK CODES 135 7.4.2 KERDOCK
SETS 135 7.4.3 PROPERTIES OF BINARY KERDOCK CODES 138 7.4.4 CLASSICAL
PREPARATA CODES 140 7.4.5 BASIC PROPERTIES ...-..* 141 7.4.6 PREPARATA
CODES AND HAMMING CODES 142 8 BASIC NOTIONS ON CODES OVER GALOIS RINGS
145 8.1 BASIC PROPERTIES 145 8.1.1 LINEAR CODES OVER Z P N 146 8.1.2
REED-MULLER CODES OVER Z P N 147 8.1.3 CYCLIC CODES OVER Z P » 148 8.1.4
HAMMING CODES OVER Z P N 151 8.2 LINEAR QUATERNARY CODES 152 8.3 KERDOCK
AND PREPARATA CODES REVISITED 158 BIBLIOGRAPHY 167 INDEX 173
|
| adam_txt |
FINITE COMMUTATIVE RINGS AND THEIR APPLICATIONS GILBERTO BINI UNIVERSITY
OF MICHIGAN U.S.A. FLAMINIO FLAMINI UNIVERSITA DEGLI STUDI ROMA TRE
ITALY KLUWER ACADEMIC PUBLISHERS BOSTON / DORDRECHT / LONDON CONTENTS
FOREWORD VII PREFACE IX FUNDAMENTAL NOTIONS IN RING THEORY 1 1.1 BASIC
DEFINITIONS 1 1.2 PRIME AND MAXIMAL IDEALS 3 1.3 EUCLIDEAN DOMAINS,
P.I.D.'S AND U.F.D.'S 9 1.4 FACTORIZATION IN Z P N[X] 20 FINITE FIELD
STRUCTURE 29 2.1 BASIC PROPERTIES 29 2.2 CHARACTERIZATION OF FINITE
FIELDS 31 2.3 GALOIS FIELD AUTOMORPHISMS 34 FINITE COMMUTATIVE RINGS.
REGULAR POLY- NOMIALS 39 3.1 FINITE COMMUTATIVE RING STRUCTURE 39 3.2
REGULAR POLYNOMIALS IN THE RING R[X) 47 3.3 I?-ALGEBRA AUTOMORPHISMS OF
R[X] 54 3.4 FACTORIZATION IN R[X] 56 SEPARABLE EXTENSIONS OF FINITE
FIELDS AND FINITE RINGS 61 4.1 SEPARABLE FIELD EXTENSIONS 61 4.2
EXTENSIONS OF RINGS 65 4.3 * SEPARABLE EXTENSIONS OF FINITE COMMUTATIVE
LOCAL RINGS . . 67 GALOIS THEORY FOR LOCAL RINGS 71 5.1 BASIC FACTS 71
VI CONTENTS 5.2 EXAMPLES. SPLITTING RINGS 75 6 GALOIS AND QUASI-GALOIS
RINGS: STRUCTURE AND PROPERTIES 81 6.1 CLASSICAL CONSTRUCTIONS 82 6.2
GALOIS RING PROPERTIES 92 6.3 STRUCTURE THEOREMS FOR FINITE COMMUTATIVE
LOCAL RINGS . . 105 6.4 ANOTHER CLASS OF FINITE COMMUTATIVE LOCAL RINGS:
QUASI- GALOIS RINGS 107 7 BASIC NOTIONS ON CODES OVER FINITE FIELDS 121
7.1 BASIC PROPERTIES 121 7.2 SOME FAMILIES OF G-ARY CODES 122 7.2.1
LINEAR CODES 122 7.2.2 HAMMING CODES 123 7.2.3 CYCLIC CODES 124 7.2.4
REED-MULLER CODES 129 7.3 DUALITY BETWEEN CODES 130 7.4 SOME FAMILIES OF
NONLINEAR G-ARY CODES 134 7.4.1 BINARY KERDOCK CODES 135 7.4.2 KERDOCK
SETS 135 7.4.3 PROPERTIES OF BINARY KERDOCK CODES 138 7.4.4 CLASSICAL
PREPARATA CODES 140 7.4.5 BASIC PROPERTIES .-.* 141 7.4.6 PREPARATA
CODES AND HAMMING CODES 142 8 BASIC NOTIONS ON CODES OVER GALOIS RINGS
145 8.1 BASIC PROPERTIES 145 8.1.1 LINEAR CODES OVER Z P N 146 8.1.2
REED-MULLER CODES OVER Z P N 147 8.1.3 CYCLIC CODES OVER Z P » 148 8.1.4
HAMMING CODES OVER Z P N 151 8.2 LINEAR QUATERNARY CODES 152 8.3 KERDOCK
AND PREPARATA CODES REVISITED 158 BIBLIOGRAPHY 167 INDEX 173 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:18:24Z |
| indexdate | 2024-07-09T21:01:45Z |
| institution | BVB |
| isbn | 140207039X |
| language | English |
| lccn | 2002025477 |
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| physical | x, 176 p. |
| publishDate | 2002 |
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| series | The Kluwer international series in engineering and computer science |
| series2 | The Kluwer international series in engineering and computer science |
| spelling | Bini, Gilberto Verfasser aut Finite commutative rings and their applications Gilberto Bini, Flaminio Flamini ; [foreword by Dieter Jungnickel] Boston Kluwer Academic Publishers 2002 x, 176 p. txt rdacontent n rdamedia nc rdacarrier The Kluwer international series in engineering and computer science 680 Commutative rings Kommutativer Ring (DE-588)4164825-0 gnd rswk-swf Kommutativer Ring (DE-588)4164825-0 s DE-604 Flamini, Flaminio Verfasser aut The Kluwer international series in engineering and computer science 680 (DE-604)BV023545171 680 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015822803&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bini, Gilberto Flamini, Flaminio Finite commutative rings and their applications The Kluwer international series in engineering and computer science Commutative rings Kommutativer Ring (DE-588)4164825-0 gnd |
| subject_GND | (DE-588)4164825-0 |
| title | Finite commutative rings and their applications |
| title_auth | Finite commutative rings and their applications |
| title_exact_search | Finite commutative rings and their applications |
| title_exact_search_txtP | Finite commutative rings and their applications |
| title_full | Finite commutative rings and their applications Gilberto Bini, Flaminio Flamini ; [foreword by Dieter Jungnickel] |
| title_fullStr | Finite commutative rings and their applications Gilberto Bini, Flaminio Flamini ; [foreword by Dieter Jungnickel] |
| title_full_unstemmed | Finite commutative rings and their applications Gilberto Bini, Flaminio Flamini ; [foreword by Dieter Jungnickel] |
| title_short | Finite commutative rings and their applications |
| title_sort | finite commutative rings and their applications |
| topic | Commutative rings Kommutativer Ring (DE-588)4164825-0 gnd |
| topic_facet | Commutative rings Kommutativer Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015822803&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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