  The extended W-algebra of type sl_2 at positive rational level, denoted by
M_{p_+,p_-}, is a vertex operator algebra that was originally proposed in [1].
This vertex operator algebra is an extension of the minimal model vertex
operator algebra and plays the role of symmetry algebra for certain logarithmic
conformal field theories. We give a construction of M_{p_+,p_-} in terms of
screening operators and use this construction to prove that M_{p_+,p_-}
satisfies Zhu's c_2-cofiniteness condition, calculate the structure of the zero
mode algebra (also known as Zhu's algebra) and classify all simple
M_{p_+,p_-}-modules.
