Holdings: Finite commutative rings and their applications

Finite commutative rings and their applications:

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Bibliographic Details
Main Authors:	Bini, Gilberto (Author), Flamini, Flaminio (Author)
Format:	Book
Language:	English
Published:	Boston Kluwer Academic Publishers 2002
Series:	The Kluwer international series in engineering and computer science 680
Subjects:	Commutative rings Kommutativer Ring
Online Access:	Inhaltsverzeichnis
Physical Description:	x, 176 p.
ISBN:	140207039X

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MARC


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Record in the Search Index

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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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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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