同余保持、格与可识别性
Congruence Preservation, Lattices and Recognizability
摘要：
看看一些monoid和（半）环（自然数，整数和p-adic整数），更一般地说，剩余有限代数（在强意义上），我们证明了两种方式的等价性，这样的代数上的函数表现得像代数的操作。第一种方法是保持同余或稳定前序。第二种方法是要求可识别集合的原像属于格或由可识别集合的原像通过代数的导出一元运算（如平移、逆变换、. . . ).
英文摘要：
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,. . . ).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
