THE STRUCTURE THEORY of non-commutative rings falls naturally into
three parts: the study of semi-simple rings; the study of radical rings;
and the construction of rings with a given radical and semi-simple
factor ring. The first of these problems has been handled by far the
most successfully. This book is intended to add to the understanding
of the second problem by presenting for the first time a unified treatment
of most of the significant known results about nilpotent rings and
algebras.
Author(s): Robert L. Price, David T. Kruse
Edition: 1
Publisher: Gordon and Breach
Year: 1969
Language: English
Commentary: 2-level bookmarks, pagination
Pages: 134
CHAPTER I Elementary results
1 Definitions and notation
2 Annihilators
3 Annihilator series
4 Subdirectly irreducible nilpotent rings
5 The primary decomposition
6 The circle group
CHAPTER II Examples of nilpotent rings
1 Representations and rings of matrices
2 Free rings
3 The construction of rings by generators and relations
4 Modular group algebras of p-groups
CHAPTER III Families and capability
1 The family classification
2 On the rings in a family
3 An example: the nilpotent rings of order p^3
4 Nilpotent rings with chain conditions
5 Capability; the construction of families
6 Conditions for capability
CHAPTER IV The subring saud11re of nilpotent rings
1 On generating rings
2 Automorphisms
3 Enumeration results
4 Nilpotent rings with only one subring of a given order
5 Nilpotent p-rings with one subring of order p
6 Rings in which all subrings are ideals
CHAPTER V Counting finite nilpotent rings
1 Introduction
2 Asymptotic results
3 Asymptotic results for non-nilpotent rings
CHAPTER VI APPENDIX The construction of some special rings
1 Some nilpotent p-rings of rank 2
2 The nilpotent algebras of dimensions 4
3 Assume dim A = 4, A^3 ≠ 0
4 Assume dim A = 4, dim A^2 = 1, A^3 = 0, and A is not reducible
5 Assume dim A = 4, dim A^2 = 2, A^3 = 0
Bibliography
List of special notation
Index
