  By giving some equivalent definitions of fractional Brauer configuration
algebras of type S in some special cases, we construct a fractional Brauer
configuration from any monomial algebra. We show that this algebra is
isomorphic to the trivial extension of the given monomial algebra. Moreover, we
show that there exists a one-to-one correspondence between the isomorphism
classes of monomial algebras and the equivalence classes of pairs consisting of
a symmetric fractional Brauer configuration algebra of type S with trivial
degree function and a given admissible cut over it.
