We consider functions of k-valued logic closed with respect to superposition classes containing all functions linear modulo k (these classes are related to divisors d of number k). Canonical relations are determined for the elements in such classes, and complete systems and bases are found. The lattice of the introduced classes with respect to the inclusion relation is described. Earlier results are generalized and complemented. This is true in particular for results on d-periodic functions and preservation of d-differences.

中文翻译：

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k值逻辑中的封闭类族

我们考虑到k值逻辑的函数相对于包含所有线性模k函数的叠加类是闭合的（这些类与数k的除数d相关）。确定此类类中元素的规范关系，并找到完整的系统和基础。描述了关于包含关系的引入类别的晶格。较早的结果得到了概括和补充。这尤其对结果真正d为周期函数和保存d -differences。