A Note on Complex Algebras of Semigroups
A Note on Complex Algebras of Semigroups
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关于半群复代数的注记
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
P. Jipsen
中科院分区：
文献类型：
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作者：
P. Jipsen
主要结果是（交换）半群的复代数所产生的变化不是有限基的。证明了这种变化与部分（交换）半群的复代数所产生的变化是一致的。给出了一个8元交换布尔半群的例子，但它不属于这一类，并对所有较小的布尔半群进行了分析，表明没有较小的例子。然而，如果没有结合律，情况就大不相同了：由（可交换）二元的复代数生成的变化是有限基的，等于所有具有（可交换）二元算子的布尔代数的变化。
The main result is that the variety generated by complex algebras of (commutative) semigroups is not finitely based. It is shown that this variety coincides with the variety generated by complex algebras of partial (commutative) semigroups. An example is given of an 8-element commutative Boolean semigroup that is not in this variety, and an analysis of all smaller Boolean semigroups shows that there is no smaller example. However, without associativity the situation is quite different: the variety generated by complex algebras of (commutative) binars is finitely based and is equal to the variety of all Boolean algebras with a (commutative) binary operator.