دانلود کتاب Nilpotent Rings

فهرست مطالب :

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