Morita系统环上的可加映射

1 Definitions and Examples of Morita Context Rings

1.1 Definitions of Morita context rings

1.2 Classical matrix algebras

1.2.1 Full matrix algebras

1.2.2 Triangular matrix algebras

1.2.3 Block upper triangular matrix algebras

1.2.4 Inflated algebras

1.3 Quasi-hereditary algebras

1.3.1 Basic construction

1.3.2 Dual extension algebras

1.4 Two non-degenerate examples

1.4.1 Morita context rings from smash product

1.4.2 Morita context rings from group algebras

1.5 Examples of operator algebras

1.5.1 Triangular Banach algebras

1.5.2 Nest algebras

1.5.3 von Neumann algebras

1.5.4 Incidence algebras

2 Linear Mappings on Morita Context Rings

2.1 Commuting mappings on Morita context rings

2.1.1 Posner Theorem

2.1.2 Commuting mappings and centralizing mappings

2.1.3 Skew muting and skew centralizing mappings

2.2 Lie derivations on Morita context rings

2.3 Jordan derivations on Morita context rings

2.4 Jordan generalized derivations on triangular algebras

2.5 Lie triple derivations on triangular algebras

2.5.1 Proof of the main Theorem

2.5.2 Another look to Theorem

2.6 Local actions of linear mappings on Morita context rings

3 Non-linear Mappings and Higher Mappings

3.1 Characterization of Jordan higher derivations

3.2 Jordan higher derivations off some operator algebras

3.3 Jordan higher derivations on triangular algebras

3.4 When a higher derivation is inner

3.5 Non-linear Lie higher derivations

3.6 Non linear Jordan bijective mappings

3.7 Jordan higher derivable points

Bibliography

The book is divided into three chapters. We begin with the definition of Morita context rings in Chapter 1, then list examples from classical matrix algebras, path algebras, smash product, groups algebras and operator algebras. In Chapter 2, we study linear mappings on Morita context rings, including commuting mappings, Lie derivations, Jordan derivations, Jordan generalized derivations and Lie triple derivations. Chapter 3 is devoted to the treatment of higher derivations and non-linear mappings.