On the Z_2-graded codimensions of the Grassmann algebra over a finite   field
  Let E be the infinite dimensional Grassmann algebra over a finite field F of characteristic not 2. In this paper we deal with the homogeneous Z_2-gradings of E. In particular, we compute an exact value for the Z_2-graded homogeneous codimensions of E, and a lower and an upper bound for the Z_2-graded (non-homogeneous) codimensions of E for each of its Z_2-homogeneous grading. 
Lucio Centrone, Lu\'is Felipe Fonseca Gon\c{c}alves
math.RA