On dominions of certain ample monoids

Abstract

A semigroup S is called left ample if it can be embedded in the symmetric inverse semigroup IX of partial bijections of a non-empty set X such that the image of S is closed under the unary operation α → αα⁻¹, where α⁻¹ is the inverse of α in IX. Right ample semigroups are defined dually. A semigroup is called ample if it is both left and right ample. A monoid is (left, right) ample if it is (left, right) ample as a semigroup. We observe that the dominion of an ample subsemigroup of IX coincides with the inverse subsemigroup of IX generated by it. We then determine the dominions of certain submonoids of In, the symmetric inverse semigroup over a finite chain 1<2<⋯

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在某些充足的一元群的领地上

如果一个半群S能嵌入到非空集合X的偏二射的对称逆半群IX中，使得S的像在一元运算α→αα⁻¹下闭，其中α⁻¹是α在IX中的逆，则称为左足半群S。右样本半群是对偶定义的。如果一个半群同时是左充足和右充足的，则称为充足。如果一个单群作为半群是(左，右)充裕的，那么它就是(左，右)充裕的。我们观察到IX的一个样本子半群的领地与它所生成的IX的逆子半群重合。然后，我们确定了有限链1<2<⋯<n上的对称逆半群In的某些子半群的域。

本文章由计算机程序翻译，如有差异，请以英文原文为准。