基于旋转群代数，以航天器姿态控制研究为背景，提出了四元数的核心矩阵的概念。

A concept of kernel matrix of quaternion is proposed, which is based on rotation group algebra and with spacecraft attitude control as its background.

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半群平移壳理论是半群代数理论的一个重要部分，在半群的理想扩张理论中占有重要地位。

The theory of translational hull of semigroups is an important branch of the algebra theory and plays a basic role in the theory of ideal extensions of semigroups.

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本文通过对合交换半群概念的引入，对MV -代数建立了几组等价公理系，对原有的公理系进行了较好的简化。

In this paper, we introduce the notion of involution commutative semi-group, and give some equivalence axioms of MV - algebras.

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