Homomorphisms of relational systems and the corresponding groupoids
نویسندگان
چکیده
A nearlattice is a meet semilattice A in which every initial segment Ap := {x : x ≤ p} happens to be a join semilattice (hence, a lattice) with respect to the natural ordering of A. If all lattices Ap are distributive, the nearlattice itself is said to be distributive. It is known that a distributive nearlattice can be represented as a nearlattice of sets. We call an algebra (A,∧,∨) of type (2,2) an augmented nearlattice if the following holds:
منابع مشابه
Ideal of Lattice homomorphisms corresponding to the products of two arbitrary lattices and the lattice [2]
Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...
متن کاملC*-algebras on r-discrete Abelian Groupoids
We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...
متن کاملSELECTIVE GROUPOIDS AND FRAMEWORKS INDUCED BY FUZZY SUBSETS
In this paper, we show that every selective groupoid induced by a fuzzy subset is a pogroupoid, and we discuss several properties in quasi ordered sets by introducing the notion of a framework.
متن کاملFuzzy homomorphisms of algebras
In this paper we consider fuzzy relations compatible with algebraic operations, which are called fuzzy relational morphisms. In particular, we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations, called uniform fuzzy relational morphisms, and those which are partially uniform F -functions, called fuzzy homomorphisms. Both uniform fuzzy relations and partially...
متن کاملFuzzy Relational Matrix-Based Stability Analysis for First-Order Fuzzy Relational Dynamic Systems
In this paper, two sets of sufficient conditions are obtained to ensure the existence and stability of a unique equilibrium point of unforced first-order fuzzy relational dynamical systems by using two different approaches which are both based on the fuzzy relational matrix of the model.In the first approach, the equilibrium point of the system is one of the centers of the related membership fu...
متن کامل