In this work we introduce the notion of fuzzy congruence relation on an ndgroupoid and study conditions on the nd-groupoid which guarantee a complete lattice structure on the set of fuzzy congruence relations. The study of these conditions allowed to construct a counterexample to the statement that the set of fuzzy congruences on a hypergroupoid is a complete lattice.

Let f be an integer greater than one. Type-f surgery is a kind of surgery along a knot in a 3-manifold which generalizes the notion of n/f surgery in a homology sphere. Such surgeries preserves the cohomology groups with Zf coefficients. Type-f surgery generates an equivalence relation on 3manifolds which we call similarity modulo f . If f is odd, we show that typef surgery also preserves the c...

Based on the light relation between a normal subgroup and a complete congruence relation of a group, we consider the homomorphism problem of rough groups and rough quotient groups and investigate their operational properties. Some new results are obtained.

One can attempt to solve the problem of establishing the correctness of some software w.r.t. a formal speciication at the semantical level. For this purpose, the semantics of an algebraic speciication should be the class of all algebras which correspond to the correct realizations of the speciication. We approach this goal by deening an observational satisfaction relation which is less restrict...

The number of distinct operations (that is, the range of the variable a) may be infinite, but for our main result (Theorem 2), we shall require every n(a) to be finite—that is, it will concern algebras with finitary operations. The concepts of subalgebra, congruence relation on an algebra, homomorphism of one algebra A onto (or into) another algebra with the same operations, and of the direct u...

We present an algorithm for the inference of some Multiple Context-Free Grammars from Membership and Equivalence Queries, using the Minimally Adequate Teacher model of Angluin. This is an extension of the congruence based methods for learning some Context-Free Grammars proposed by Clark (ICGI 2010). We define the natural extension of the syntactic congruence to tuples of strings, and demonstrat...

We obtain relations between the modular degree and congruence modulus of elliptic curves, and answer a question raised in a paper of Frey and Müller about whether or not the congruence number and modular degree of elliptic curves are always equal; they are not, but we give a conjectural relation between them. We also prove results and make conjectures about Manin constants of quotients of J1(N)...

In 7] a hierarchy of directed acyclic graph (dag) algebras is deened. The dags belonging to an algebra are deened up to an isomorphism which can be expressed by a congruence over a free term algebra, i.e. a dag is described by a congruence class of terms. In this paper we deal with the following problem: can be deened a canonical form in every congruence class and a canonical (connuent and term...

We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propo...