On Centrally Essential Subrings of Formal Triangular Matrix Rings

A ring $R$ with a non-zero identity element is said to be centrally essential if for any non-zero element $a\in R$, there exist non-zero central elements $x,y\in R$ such that $ax = y$. We describe centrally essential rings in a large subclass of formal triangular matrix rings and in a subclass of the matrix ring $M_3(R)$ over the ring $R$.