The lattice of pseudovarieties of idempotent semigroups and a non-regular analogue
The lattice of pseudovarieties of idempotent semigroups and a non-regular analogue
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幂等半群和非正则类似物的伪簇格
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发表时间：
1997
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通讯作者：
Pascal Weil
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作者：
P. G. Trotter;Pascal Weil
抽象。我们在格上使用经典的结果
$ cal L（cal B）$的带（幂等）半群簇的格P_s（DA）的结构信息，其中DA是有限半群的最大伪簇，其中所有正则半群都是带半群.本文提出了Ps（DA）上的一个格同余，它的商同构于
$ cal L，（cal B）$，其类是具有有效可计算的最小和最大成员的区间。最后，设Vk是DA的k-生成元生成的伪簇（k≥ 1），我们利用我们的结果计算了Vk的同余类在DA中的位置。
$校准L（校准B）$。
Abstract. We use classical results on the lattice
$ cal L (cal B) $ of varieties of band (idempotent) semigroups to obtain information on the structure of the lattice Ps (DA) of subpseudovarieties of DA, – where DA is the largest pseudovariety of finite semigroups in which all regular semigroups are band semigroups. We bring forward a lattice congruence on Ps (DA), whose quotient is isomorphic to
$ cal L, (cal B) $, and whose classes are intervals with effectively computable least and greatest members. Also we characterize the pro-identities satisfied by the members of an important family of subpseudovarieties of DA. Finally, letting Vk be the pseudovariety generated by the k-generated elements of DA (k≥ 1), we use all our results to compute the position of the congruence class of Vk in
$ cal L (cal B ) $.