We give a thorough structural analysis of the principal one-sided ideals of arbitrary semigroups, and then apply this to full transformation semigroups and symmetric inverse monoids. One-sided ideals of these semigroups naturally occur as semigroups of transformations with restricted range or kernel.

中文翻译：

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主要片面理想的结构

我们对任意半群的主要单面理想进行了彻底的结构分析，然后将其应用于全变换半群和对称逆幺半群。这些半群的片面理想自然地作为具有受限范围或核的变换的半群出现。