Completely regular semigroups with the unary operation of inversion within their maximal subgroups form a variety under inclusion denoted by $$\mathcal {C}\mathcal {R}$$ C R . The lattice of its subvarieties is denoted by $$\mathcal {L}(\mathcal {C}\mathcal {R})$$ L ( C R ) . Kernel, trace, left trace and right trace relations on $$\mathcal {L}(\mathcal {C}\mathcal {R})$$ L ( C R ) induce operators which can be used to produce networks. For the pairs (kernel, trace)- and (left trace, right trace)-networks we establish strong properties. We consider examples of local- and core-relations networks in some special cases, as well as $$\mathbf {B}^\wedge \mathbf {B}^\vee $$ B ∧ B ∨ -networks.

中文翻译：

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在完全正则半群的变体的某些区间上

完全正则半群在它们的最大子群内具有一元求逆运算，在包含下形成一个变体，用 $$\mathcal {C}\mathcal {R}$$ CR 表示。其子变体的格由 $$\mathcal {L}(\mathcal {C}\mathcal {R})$$ L ( CR ) 表示。$$\mathcal {L}(\mathcal {C}\mathcal {R})$$ L ( CR ) 上的核、迹、左迹和右迹关系归纳出可用于生成网络的算子。对于（内核，跟踪）和（左跟踪，右跟踪）对网络，我们建立了强大的属性。我们考虑一些特殊情况下的本地和核心关系网络的例子，以及 $$\mathbf {B}^\wedge \mathbf {B}^\vee $$ B ∧ B ∨ -networks。