Verfügbarkeit: Nilpotent rings | Technische Universität München

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Bibliographische Detailangaben
Beteiligte Personen:	Kruse, Robert L. (VerfasserIn), Price, David T. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Gordon and Breach 1969
Schriftenreihe:	Notes on mathematics and its applications
Schlagwörter:	Anneaux (Mathématiques) Rings (Algebra) Nilpotenter Ring
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001848696&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	VIII, 127 S. Ill.

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adam_text	Contents Preface ........ v Chapter I Elementary results ...... 1 1 Definitions and notation 1 2 Annihilators 2 3 Annihilator series 4 4 Subdirectly irreducible nilpotent rings 7 5 The primary decomposition 9 6 The circle group 10 Chapter II Examples of nilpotent rings .... 17 1 Representations and rings of matrices 17 2 Free rings 19 3 The construction of rings by generators and relations 20 4 Modular group algebras of ^ groups 24 Chapter III Families and capability ..... 27 1 The family classification 27 2 On the rings in a family 29 3 An example: the nilpotent rings of order p3 34 4 Nilpotent rings with chain conditions 40 5 Capability; the construction of families 42 6 Conditions for capability 48 Chapter IV The sabring structure of nilpotent rings . . 51 1 On generating rings 51 2 Automorphisms 54 3 Enumeration results 59 4 Nilpotent rings with only one subring of a given order 62 vii Vlii CONTENTS 5 Nilpotent p rings with one subring of order p 67 6 Rings in which all subrings are ideals 68 Chapter V Counting finite nilpotent rings .... 80 1 Introduction 80 2 Asymptotic results 81 3 Asymptotic results for non nilpotent rings 90 Chapter VI Appendix The construction of some special rings 95 1 Some nilpotent ^ rings of rank 2 95 2 The nilpotent algebras of dimensions 4 99 3 Assume dim A = 4, A3 ^ 0 101 4 Assume dim A = 4, dim A2 == 1, A3 = 0, and A is not reducible 102 5 Assume dim A = 4, dim A2 = 2, A3 = 0 104 Bibliography . . . . . . .109 List of special notation . . . . .123 Index 125
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spellingShingle	Kruse, Robert L. Price, David T. Nilpotent rings Anneaux (Mathématiques) Rings (Algebra) Nilpotenter Ring (DE-588)4589834-0 gnd
subject_GND	(DE-588)4589834-0
title	Nilpotent rings
title_auth	Nilpotent rings
title_exact_search	Nilpotent rings
title_full	Nilpotent rings Robert L. Kruse and David T. Price
title_fullStr	Nilpotent rings Robert L. Kruse and David T. Price
title_full_unstemmed	Nilpotent rings Robert L. Kruse and David T. Price
title_short	Nilpotent rings
title_sort	nilpotent rings
topic	Anneaux (Mathématiques) Rings (Algebra) Nilpotenter Ring (DE-588)4589834-0 gnd
topic_facet	Anneaux (Mathématiques) Rings (Algebra) Nilpotenter Ring
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work_keys_str_mv	AT kruserobertl nilpotentrings AT pricedavidt nilpotentrings

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