# Ideals and finiteness conditions for subsemigroups

Gray, Robert, Maltcev, V, Mitchell, JD and Ruskuc, N (2014) Ideals and finiteness conditions for subsemigroups. Glasgow Mathematical Journal, 56 (01). pp. 65-86. ISSN 0017-0895

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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, $\mathcal{D}=\mathcal{J}$ and minimal conditions on ideals.