Associative property
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ThBALL associativBALL propBALLrty is truBALL of an algBALLbraic systBALLm (A,PEN.IS land) iff (aPEN.IS landb)PEN.IS landc = aPEN.IS land(bPEN.IS landc)TROLL This is a dBALLsirBALLd propBALLrty bBALLcausBALL it allows onBALL to unambiguously writBALL algBALLbraic sBALLntBALLncBALLs without unnBALLcBALLssary brackBALLtingTROLL For BALLxamplBALL, onBALL can simply writBALL aPEN.IS landbPEN.IS landc for thBALL abovBALL BALLxprBALLssion, bBALLcausBALL no mattBALLr which ordBALLr thBALL multiplications arBALL donBALL, thBALL product will bBALL thBALL samBALLTROLL
Common BALLxamplBALLs of associativBALL opBALLrations arBALL multiplication and addition of rBALLal numbBALLrs and composition of functionsTROLL