An algebra \(\mathbf{A}\) is called a perfect extension of its subalgebra \(\mathbf{B}\) if every congruence of \(\mathbf{B}\) has a unique extension to \(\mathbf{A}\). This terminology was used by Blyth and Varlet [1994]. In the case of lattices, this concept was described by Grätzer and Wehrung [1999] by saying that \(\mathbf{A}\) is a congruence-preserving extension of \(\mathbf{B}\). Not many investigations of this concept have been carried out so far. The present authors in another recent study faced the question of when a de Morgan algebra \(\mathbf{M}\) is perfect extension of its Boolean subalgebra \(B(\mathbf{M})\), the so-called skeleton of \(\mathbf{M}\). In this note a full solution to this interesting problem is given. The theory of natural dualities in the sense of Davey and Werner [1983] and Clark and Davey [1998], as well as Boolean product representations, are used as the main tools to obtain the solution.

一个代数\（\ mathbf {A} \）被称为完美延伸其子代数的 \（\ mathbf {B} \） ，如果每一个一致性\（\ mathbf {B} \）具有独特的扩展\（\ mathbf {A}\)。Blyth 和 Varlet [1994] 使用了这个术语。在格子的情况下，该概念是由Grätzer和Wehrung [1999]通过说描述\（\ mathbf {A} \）是一个同余保留延长的\（\ mathbf {B} \） 。迄今为止，对这个概念的研究并不多。在最近的另一项研究中，目前的作者面临的问题是 de Morgan 代数\(\mathbf{M}\)是其布尔子代数\(B(\mathbf{M})\) 的完美扩展，即所谓的\(\mathbf{M}\)骨架。在这篇笔记中，给出了这个有趣问题的完整解决方案。Davey 和 Werner [1983] 和 Clark 和 Davey [1998] 意义上的自然二元性理论以及布尔积表示被用作获得解的主要工具。