We completely determine all varieties of monoids on whose free objects all fully invariant congruences or all fully invariant congruences contained in the least semilattice congruence permute. Along the way, we find several new monoid varieties with the distributive subvariety lattice (only a few examples of varieties with such a property are known so far).

中文翻译：

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幺半群变体的同余置换性的两个较弱变体

我们完全确定所有种类的幺半群，其自由对象上的所有完全不变同余或包含在最小半格同余置换中的所有完全不变同余。一路上，我们发现了几个新的具有分配子变体格的幺半群变体（到目前为止，只有少数具有这种性质的变体的例子是已知的）。