  The concept of a state MV-algebra was firstly introduced by Flaminio and
Montagna in \cite{FlMo0} and \cite{FlMo} as an MV-algebra with internal state
as a unary operation. Di Nola and Dvure\v{c}enskij gave a stronger version of a
state MV-algebra in \cite{DiDV1}, \cite{DiDV2}. In the present paper we
introduce the notion of a state BL-algebra, or more precisely, a BL-algebra
with internal state. We present different types of state BL-algebras, like
strong state BL-algebras and state-morphism BL-algebras, and we study some
classes of state BL-algebras. In addition, we give a sample of important
examples of state BL-algebras and present some open problems.
