This paper is devoted to study the notion of state Rl monoids and to investigate their properties.
We establish a connection between (normal) ?-filters of a state Rl monoid A_V and (normal) filters of Rl
monoid ?(A). We characterize simple and local state R‘ monoids. Also, we make a correction on the
proof of [3, Theorem 4.11] for characterization of subdirectly irreducible state R‘ monoids.