Ideals and finiteness conditions for subsemigroups
  In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroups with finite Rees or Green index. Specific properties under consideration include stability, D=J and minimal conditions on ideals. 
R. Gray, V. Maltcev, J. D. Mitchell, N. Ruskuc
math.GR