xayxxa = xayxxayxya = yayxyaxyya = yaxyyaxyxa = xaxy

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- Jun 1st 2010, 03:32 PMkiwijoeySemigroups: Do the following 4 equations imply x=y?
xayxxa = xayxxayxya = yayxyaxyya = yaxyyaxyxa = xaxy

- Jun 1st 2010, 03:34 PMkiwijoey
Why didn't that post correctly?Equation 1: xayxxa = xayxEquation 2: xayxya = yayxEquation 3: yaxyya = yaxyEquation 4: yaxyxa = xaxy

- Jun 2nd 2010, 12:37 AMSwlabr
Well...no. Every relation is of the form $\displaystyle u=v$ where $\displaystyle |u| = 6$ and $\displaystyle |v|=4$. As you are in a semigroup there is no way of getting a relation of the form $\displaystyle u=v$ where $\displaystyle |u|=1=|v|$ as you cannot cancel anything.

What do you mean by the element $\displaystyle a$?