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1、CourseMA2C01,MichaelmasTerm2009Section3:AbstractAlgebraDavidR.WilkinsCopyrightcDavidR.Wilkins2000{2009Contents3AbstractAlgebra323.1BinaryOperationsonSets....................323.2CommutativeBinaryOperations................323.3AssociativeBinaryOperations..................323.4Semigroups.....
2、.......................333.5TheGeneralAssociativeLaw..................343.6Identityelements.........................353.7Monoids..............................353.8Inverses..............................363.9Groups...............................393.10HomomorphismsandIsomorphisms..............
3、.41i3AbstractAlgebra3.1BinaryOperationsonSetsDe nitionAbinaryoperationonasetAisanoperationwhich,whenappliedtoanyelementsxandyofthesetA,yieldsanelementxyofA.ExampleThearithmeticoperationsofaddition,subtractionandmultipli-cationarebinaryoperationsonthesetRofrealnumberswhich,whenap-pliedtore
4、alnumbersxandy,yieldtherealnumbersx+y,x
