Have the semigroups with the following cancellation property been studied?
Property: Let $S$ be a semigroup and $x,y\in S$ such that $xz=yz,$ for all $z\in S,$ then $x=y$.
$\begingroup$
$\endgroup$
4
-
$\begingroup$ Obvious remark: for monoids this is trivial (taking $z=1$). $\endgroup$– Sam HopkinsCommented Jul 10 at 15:07
-
$\begingroup$ Other obvious remark: if one writes $R_z(x)=xz$, this is the requirement of injectivity of $z\mapsto R_z$. And obvious example where it fails: set with an element $0$ and not reduced to $\{0\}$, with constant law $xy=0$ $\forall x,y$. $\endgroup$– YCorCommented Jul 10 at 15:09
-
3$\begingroup$ This seems to be called a right reductive semigroup, at least on Wikipedia and nLab. $\endgroup$– Naïm FavierCommented Jul 10 at 15:21
-
$\begingroup$ @NaïmFavier Thanks, that is exactly what i was looking for. $\endgroup$– Hector PinedoCommented Jul 10 at 16:38
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
