We describe acts over rectangular bands that have modular, distributive or linearly ordered congruence lattice. It turns out that such acts have at most 11 elements, and their congruence lattice has at most 300 elements. Furthermore, certain facts are established about the structure of acts with modular congruence lattice over an arbitrary semigroup and about the structure of the congruence lattice of an act over a rectangular band. The work is based on the description of acts over a completely (0-)simple semigroup obtained by Avdeev and Kozhukhov in 2000 and on the characterization of disconnected acts with modular or distributive congruence lattice by Ptakhov and Stepanova in 2013.

中文翻译：

---

矩形带上一个动作的全等格的模数条件

我们描述了具有模块化，分布式或线性有序全等格子的矩形带上的行为。事实证明，这种行为最多包含11个元素，它们的全等格最多包含300个元素。此外，关于在任意半群上具有模块同余格的行为的结构以及在矩形带上的行为同余格的结构，已经确定了某些事实。该工作基于对由Avdeev和Kozhukhov在2000年获得的完全（0-）简单半群上的行为的描述，以及基于Ptakhov和Stepanova在2013年对具有模块化或分布同余格的不连续行为的表征。