AUTOMATIC CLIFFORD SEMIGROUPS
AUTOMATIC CLIFFORD SEMIGROUPS
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自动克利福德半群
DOI：
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发表时间：
2010
期刊：
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通讯作者：
Alan J. Cain
中科院分区：
文献类型：
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作者：
Alan J. Cain
研究了具有自动结构的Clifford半群（群的强半格）.证明了一个自动半群是否是Clifford半群是可判定的。给出了Clifford半群自动结构的一个几何刻画。自动群的一些性质，如有限可表示性，允许前缀闭自动结构，以及自动性在生成元变化下的不变性，被推广到Clifford半群上.研究了由自由群的强半格或交换群的强半格构成的Clifford半群是自动半群的条件。
A study is made of Clifford semigroups (strong semilattices of groups) admitting automatic structures. It is shown to be decidable whether an automatic semigroup is a Clifford semigroup. A geometric characterization of automatic structures for Clifford semigroups is developed. Some properties of automatic groups, such as finite presentability, admitting a prefix-closed automatic structure, and invariance of automaticity under change of generators, are found to generalize to Clifford semigroups. Conditions are investigated under which a Clifford semigroup consisting of a strong semilattices of free groups or a strong semilattices of abelian groups is automatic.