ipsilaterally
It is the cerebellar vermis.
The transverse fissure.
Falx Cerebelli.
vermis
The falx cerebelli invaginates into the cerebellar notch between the two cerebellar hemispheres. It doesn't actually separate the two hemispheres though. The falx cerebri separates the two cerebral hemispheres.
The cerebral hemispheres are connected by the corpus callosum.
The structure you are referring to is the falx cerebelli. It is a tent-like fold of the dura mater that lies between the cerebellar hemispheres and helps to stabilize and protect the brain.
corpus callosum
The cortex is divided into two sections referred to as the cerebral cortex and the cerebellar cortex.
a large portion of the brain, serving to coordinate voluntary movements, posture, and balance in humans, being in back of and below the cerebrum and consisting of two lateral lobes and a central lobe.
The pons connects the cerebrum to the cerebellum. The cerebellum is responsible for the motor control in the brain.
The middle cerebellar peduncle is the thickest of the three cerebellar peduncles. It is the largest and most prominent of the three, connecting the cerebellum to the brainstem and allowing for communication between the cerebellum and other parts of the brain.