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 commuting 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 2.5.1
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
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