We consider semigroups strongly Morita equivalent to a fixed monoid. We prove that such semigroups are precisely the enlargements of that monoid. We also show that enlargements of a given group are precisely the Rees matrix semigroups over that group.

中文翻译：

---

半群强森田等价于幺半群

我们认为半群 Morita 等价于固定幺半群。我们证明这样的半群正是那个幺半群的扩大。我们还表明，给定群的扩大恰好是该群上的里斯矩阵半群。