On the Finite and Nonfinite Generation of Diagonal Acts
On the Finite and Nonfinite Generation of Diagonal Acts
复制标题
论对角线的有限和非有限生成
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. Gallagher
中科院分区：
文献类型：
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作者：
P. Gallagher
半群S的对角右系是集合S × S，其中S从右起按分量相乘。S的对角左系和对角双系的定义类似。给出了完全零单半群和完全单半群的对角双系有限生成的充要条件。它还证明了各种类型的半群不具有循环生成或循环对角右，左，或双作用。
The diagonal right act of a semigroup S is the set S × S, with S acting by componentwise multiplication from the right. The diagonal left act and diagonal bi-act of S are defined analogously. Necessary and sufficient conditions are found for the finite generation of the diagonal bi-acts of completely zero-simple semigroups and completely simple semigroups. It is also proved that various classes of semigroups do not have finitely generated or cyclic diagonal right, left, or bi-acts.