Given any amalgam [S1,S2; U] of inverse semigroups, we show how to construct an amalgam [T1,T2; Z] such that S1 ∗US2 is embedded into T1 ∗ZT2, where S1 ⊆ T1, S2 ⊆ T2, S1 ∩ Z = S2 ∩ Z = U and, for any z ∈ Z and h ∈ E(Ti) with z ≥ h in Ti, where i ∈{1, 2}, there exists f ∈ E(Z) with z ≥ f ≥ h in Ti; that is, Z is a lower bounded subsemigroup of T1 and T2. A recent paper by the author describes the Schützenberger automata of T1 ∗ZT2, for an amalgam [T1,T2; Z] where Z is lower bounded in T1 and T2, giving conditions for T1 ∗ZT2 to have decidable word problem. Thus we can study S1 ∗US2 by considering T1 ∗ZT2. As an example, we generalize results by Cherubini, Jajcayová, Meakin, Piochi and Rodaro on amalgams of finite inverse semigroups.

中文翻译：

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反半群的汞合金嵌入到具有下界核心的汞合金中

给定任何汞合金[小号1,小号2; ü]逆半群，我们展示了如何构造一个汞齐[吨1,吨2; Z]这样小号1 *ü小号2嵌入到吨1 *Z吨2， 在哪里小号1 ⊆ 吨1,小号2 ⊆ 吨2,小号1 ∩ Z = 小号2 ∩ Z = ü并且，对于任何z ∈ Z和H ∈ 乙(吨一世)和z ≥ H在吨一世， 在哪里一世 ∈{1, 2}， 那里存在F ∈ 乙(Z)和z ≥ F ≥ H在吨一世; 那是，Z是一个下界子半群吨1和吨2. 作者最近的一篇论文描述了 Schützenberger 自动机吨1 *Z吨2, 对于汞合金[吨1,吨2; Z]在哪里Z下界在吨1和吨2, 给出条件吨1 *Z吨2有可判定的单词问题。这样我们可以学习小号1 *ü小号2通过考虑吨1 *Z吨2. 例如，我们推广 Cherubini、Jajcayová、Meakin、Piochi 和 Rodaro 在有限逆半群的汞合金上的结果。