Questions tagged [finite-semigroups]

For order $2$, I have found 5. There are 16 maps from $\{a, b\} \times \{a, b\} \to\{a, b\}$. They form $10$ equivalence classes of non-isomorphic binary operations, $5$ of which are associative. Of these $2$ are monoids and $1$ is a group.They are…

Let $a$ and $b$ be two elements of a finite semigroup. Show that if $abb = b$, then $bab = b$. Now I did this: $abb = b$, so $bab = abbab$. But $abb = b$, so $bab = b$. I know in semigroups this doesn't work like in strings.