Abstract A formation of monoids is a class of finite monoids closed under taking quotients and subdirect products. Formations of monoids were first studied in connection with formal language theory, but in this paper, we come back to an algebraic point of view. We give two natural constructions of formations based on constraints on the minimal ideal and on the maximal subgroups of a monoid. Next we describe two sublattices of the lattice of all formations, and give, for each of them, an isomorphism with a known lattice of varieties of monoids. Finally, we study formations and varieties containing only Clifford monoids, completely describe such varieties and discuss the case of formations.

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关于幺半群的形成

摘要 幺半群的形成是一类在取商和子直积下封闭的有限幺半群。幺半群的形成首先是结合形式语言理论研究的，但在本文中，我们回到代数的观点。我们基于对幺半群的最小理想和最大子群的约束，给出了两种自然的构造构造。接下来，我们描述所有结构的格的两个亚格，并为它们中的每一个给出一个同构，与已知的幺半群变体格。最后，我们研究仅包含 Clifford 幺半群的组和变体，完整地描述这些变体并讨论组的情况。