2020/04/13 by Patrick Cégielski, Cegielski, Patrick, Serge Grigorieff +3
Computer Science · Mathematics · #03G10 #06B10 #Advanced Algebra and Logic #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO) #Rings, Modules, and Algebras #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2004.05943
openalex publication_date 2020/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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,. . . ).