Eilenberg’s variety theorem gives a bijective correspondence between varieties of languages and varieties of finite semigroups. The second author gave a similar relation between conjunctive varieties of languages and varieties of semiring homomorphisms. In this paper, we add a third component to this result by considering varieties of meet automata. We consider three significant classes of lang...

0.1. Endomorphisms of elliptic curves. Recall that a homomorphism of complex elliptic curves is just a holomorphic map E1 → E2 which preserves the origin. (It turns out that this condition is enough to force it to be a homomorphism of groups in the usual sense; why?) An isogeny of elliptic curves is a homomorphism whose kernel is a finite subgroup of E1. In fact the kernel of a homomorphism of ...

We show that for every binary matroid $N$ there is a graph $H_*$ such the graphic $M_G$ of $G$, matroid-homomorphism from to if and only graph-homomorphism $G$ $H_*$. With this we prove complexity dichotomy problem $\rm{Hom}_\mathbb{M}(N)$ deciding $M$ admits homomorphism $N$. The polynomial time solvable has loop or no circuits odd length, otherwise $\rm{NP}$-complete. also get dichotomies lis...

the starting point of this paper is given by priestley’s papers, where a theory of representation of distributive lattices is presented. the purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. in this way, some results of priestley’s papers are extended. in the main theorem, we show that the category of finite fuzzy priestley space...

For every pair of nite connected graphs F and H, and every integer k, we construct a universal graph U with the following properties: 1. There is a homomorphism : U ! H, but no homomorphism from F to U . 2. For every graph G with maximal degree no more than k having a homomorphism h : G! H, but no homomorphism from F to G, there is a homomorphism : G! U , such that h = . Particularly, this solv...