Type B semigroups are generalizations of inverse semigroups, and every inverse semigroup admits an E-unitary cover (M. Petrich, Inverse Semigroups (Wiley, New York, 1984)). Motivated by studying E-unitary cover for inverse semigroups, and as a continuation of Petrich’s works in inverse semigroups, in this paper, we first introduce the concept of ∗-prehomomorphism of a type B semigroup. After obtaining some basic properties, we get some structure theorems and give some conditions for a type B semigroup which is constructed by using the ∗-prehomomorphism to be proper. In particular, we introduce the notion of E-unitary good cover for an abundant semigroup, and prove that every type B semigroup with compatible natural partial order admits an E-unitary good cover.

中文翻译：

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B 型半群的 A ∗-前同态

B类半群是反半群的推广，每个反半群都承认一个乙-单一封面（M. Petrich，逆半群（威利，纽约，1984 年））。学习的动力乙- 反半群的酉覆盖，作为 Petrich 在反半群工作的延续，在本文中，我们首先介绍了 B 型半群的 *-前同态的概念。在获得了一些基本性质之后，我们得到了一些结构定理，并给出了用∗-前同态构造的B型半群的一些条件。特别是，我们引入了乙- 一个丰富半群的酉好覆盖，并证明每个具有兼容自然偏序的 B 型半群都承认一个乙- 单一的好封面。