Geodesic
Inverse semigroups whose full inverse subsemigroups form a chain
Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 159-165

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The structure of semigroups whose subsemigroups form a chain under inclusion was determined by Tamura [9]. If we consider the analogous problem for inverse semigroups it is immediate that (since idempotents are singleton inverse subsemigroups) any inverse semigroup whose inverse subsemigroups form a chain is a group. We will therefore, continuing the approach of [5, 6], consider inverse semigroups whose full inverse subsemigroups form a chain: we call these inverse ▽-semigroups. 
Jones, P. R. Inverse semigroups whose full inverse subsemigroups form a chain. Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 159-165. doi: 10.1017/S0017089500004626
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