Normality and Covering Properties of Affine Semigroups

  title={Normality and Covering Properties of Affine Semigroups},
  author={Winfried Bruns and Joseph Gubeladze},
S̄ = {x ∈ gp(S) | mx ∈ S for some m > 0}. One calls S normal if S = S̄. For simplicity we will often assume that gp(S) = Z; this is harmless because we can replace Z by gp(S) if necessary. The rank of S is the rank of gp(S). We will only be interested in the case in which S ∩ (−S) = 0; such affine semigroups will be called positive. The positivity of S is equivalent to the pointedness of the cone C(S) = R+S generated by S in R; one has rankS = dimC(S). (All the cones appearing in this paper… CONTINUE READING