I've isolated a property of rings (integral domains, associative, unitary, non necessarily commutative) that is useful to me :

$$xR\cap yR\neq\{0\}\quad\text{ whenever $x$ and $y$ are non zero.}$$

Question.Does this property has a name, or falls into a known and labelled class of rings ?

Commutative integral domains and division rings obviously have this property.