FREE ADEQUATE SEMIGROUPS
FREE ADEQUATE SEMIGROUPS
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DOI：
10.1017/s1446788711001753
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发表时间：
2009-02
影响因子：
0.7
通讯作者：
Mark Kambites
中科院分区：
文献类型：
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作者：
Mark Kambites
摘要给出了在自然组合乘法下，充分半群的准簇中的自由对象作为标记有向树的集合的显式描述。通过组合“折叠”运算，将我们的树转化为穆恩树，实现了自由充分半群向自由充足半群和自由逆半群的模射。利用这些结果，我们证明了自由充分半群和半群是𝒥-trivial且永远不会有限生成为半群，而有限生成为(2,1,1)-代数的半群具有可决的字问题。
Abstract We give an explicit description of the free objects in the quasivariety of adequate semigroups, as sets of labelled directed trees under a natural combinatorial multiplication. The morphisms of the free adequate semigroup onto the free ample semigroup and into the free inverse semigroup are realised by a combinatorial ‘folding’ operation which transforms our trees into Munn trees. We use these results to show that free adequate semigroups and monoids are 𝒥-trivial and never finitely generated as semigroups, and that those which are finitely generated as (2,1,1)-algebras have decidable word problem.