Right module of vertex operator algebra

This paper defines the right module of vertex operator algebra. It's well known that in the definition of left module, Jacobi identity can be replaced by commutative formula and associative formula. In this paper we give the equivalent formulas which can replace opposite Jacobi identity for right module.;We also construct a right model which is based on bimodule as an example. Given a vertex operator algebra V and associate algebras An(V) and Am( V), a bimodule An,m(V) carriers the structure of right module and left module for A n(V) and Am( V) respectively. In this paper, we prove ⨁n∈Z + U ⊗A( V) (A0, n(V)) is a right module of V, for any A(V) module U..