In the present paper, a series of results and examples that explore the structural features of $$\mathcal {H}$$ -commutative semigroups are provided. We also generalize a result of Isbell from commutative semigroups to $$\mathcal {H}$$ -commutative semigroups by showing that the dominion of an $$\mathcal {H}$$ -commutative semigroup is $$\mathcal {H}$$ -commutative. We then use this to generalize Howie and Isbell’s result that any $$\mathcal {H}$$ -commutative semigroup satisfying the minimum condition on principal ideals is saturated.

中文翻译：

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Epimorphisms, dominions 和 $$\mathcal {H}$$ H -可交换半群

在本文中，提供了一系列探索 $$\mathcal {H}$$ -可交换半群的结构特征的结果和例子。我们还通过证明 $$\mathcal {H}$$ -可交换半群的域是 $$\mathcal {H} 将 Isbell 的结果从交换半群推广到 $$\mathcal {H}$$ -交换半群$$ - 可交换的。然后我们使用它来推广 Howie 和 Isbell 的结果，即满足主理想上的最小条件的任何 $$\mathcal {H}$$ -可交换半群都是饱和的。