Abstract In this paper, we develop the elementary theory of inverse semigroups to the cases of type B semigroups. The main aim of this paper is to study proper type B semigroups. We introduce first the concept of a left admissible triple. After obtaining some basic properties of left admissible triple, we give the definition of a Q-semigroup and get a structure theorem of Q-semigroup. In particular, we introduce the notion of an admissible triple and give some characterization of proper type B semigroups. It is proved that an arbitrary Q-semigroup with an admissible triple is an E-unitary type B semigroup.

中文翻译：

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一个适当的 B 型半群的新刻画

摘要 在本文中，我们将逆半群的基本理论发展到 B 型半群的情况。本文的主要目的是研究适当的 B 型半群。我们首先介绍左可容许三元组的概念。得到左容许三元组的一些基本性质后，给出Q-半群的定义，得到Q-半群的结构定理。特别地，我们引入了可容许三元组的概念，并给出了适当的 B 型半群的一些表征。证明了具有可接纳三元组的任意Q-半群是E-幺正B型半群。