Thread: Semigroups: Do the following 4 equations imply x=y?

xayxxa = xayxxayxya = yayxyaxyya = yaxyyaxyxa = xaxy

Why didn't that post correctly?Equation 1: xayxxa = xayxEquation 2: xayxya = yayxEquation 3: yaxyya = yaxyEquation 4: yaxyxa = xaxy

Originally Posted by kiwijoey

Why didn't that post correctly?Equation 1: xayxxa = xayxEquation 2: xayxya = yayxEquation 3: yaxyya = yaxyEquation 4: yaxyxa = xaxy

Well...no. Every relation is of the form where and . As you are in a semigroup there is no way of getting a relation of the form where as you cannot cancel anything.

What do you mean by the element ?