Verfügbarkeit: Finite commutative rings and their applications

Finite commutative rings and their applications:

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Bibliographische Detailangaben
Beteiligte Personen:	Bini, Gilberto (VerfasserIn), Flamini, Flaminio (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Boston Kluwer Academic Publishers 2002
Schriftenreihe:	The Kluwer international series in engineering and computer science 680
Schlagwörter:	Commutative rings Kommutativer Ring
Links:	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
Umfang:	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
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illustrated	Not Illustrated
indexdate	2024-12-20T12:59:36Z
institution	BVB
isbn	140207039X
language	English
lccn	2002025477
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-015822803
oclc_num	49283522
open_access_boolean
owner	DE-703
owner_facet	DE-703
physical	x, 176 p.
publishDate	2002
publishDateSearch	2002
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publisher	Kluwer Academic Publishers
record_format	marc
series	The Kluwer international series in engineering and computer science
series2	The Kluwer international series in engineering and computer science
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_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
volume_link	(DE-604)BV023545171
work_keys_str_mv	AT binigilberto finitecommutativeringsandtheirapplications AT flaminiflaminio finitecommutativeringsandtheirapplications

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