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 left-right iteraton in right-divisible magmas, and fractional ranks. MphLee Fellow Posts: 95 Threads: 7 Joined: May 2013 05/14/2014, 03:51 PM first attempt to study the relation to associativity... if $*$ is associative then $L_a^{\circ n}=L_{a^n}$, where $a^n$ is defined as usual $a^1:=a$ and $a^{n+1}=a*a^n$ but if it is not associative then the existence of an injection maybe depend on the existence of a binary function $\cdot:G^2\rightarrow G$ witht his property $a*(b*x)=(a\cdot b)*x$ or in other words $L_a \circ L_b=L_{a\cdot b}$ someone knows when such operation can exist and how is called this property? When $*$ is right invertible then $a\cdot b=a*(b*x)\setminus_* x$ but I don't know when this operation becomes indipendent from $x$ MathStackExchange account:MphLee « Next Oldest | Next Newest »

 Messages In This Thread left-right iteraton in right-divisible magmas, and fractional ranks. - by MphLee - 05/13/2014, 05:32 PM RE: left-right iteraton in right-divisible magmas, and fractional ranks. - by MphLee - 05/14/2014, 03:51 PM

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