Abstract | Abstract We consider ideals in the ring Z_2 [ x_1 , … , x_n ] that contain the polynomials x_i^2 − x_i for i = 1 , … , n and give various results related to the one-to-one correspondence between these ideals and the subsets of Z 2 n . We also study the standard monomials with respect to the lexicographical ordering for these ideals and derive a distribution result. |