论文标题
一致性保存，晶格和可识别性
Congruence Preservation, Lattices and Recognizability
论文作者
论文摘要
查看一些单型和（半）环（自然数，整数和p-adic整数），以及更普遍的，残留有限的代数（从强烈的意义上），我们证明了在这种代数上的函数的两种方式与代数类似于代数的操作。第一种方法是保留一致性或稳定的预订。第二种方法是要求可识别集的预图属于晶格或由代数的派生的Unary操作（例如翻译，商，商，...）产生的可识别集产生的布尔代数。
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave like the operations of the algebra. The first way is to preserve congruences or stable preorders. The second way is to demand that preimages of recognizable sets belong to the lattice or the Boolean algebra generated by the preimages of recognizable sets by derived unary operation of the algebra (such as translations, quotients,. . . ).
