Extending Congruence Relations

Extending Congruence Relations

If 91 and 23 are algebras, where 9Is23, and 6 is a congruence relation on 91, let 0® be the smallest congruence relation on 93 containing 0. 91 is called a congruence subalgebra of 93 if 9ls93 and, for every congruence relation 0 on 91, 0*n|9I|2=0. Elementary subalgebras are congruence subalgebras, and there are Directed Union and Loewenheim-Skolem Theorems for congruence subalgebras analogous ...

Congruence Relations on Multilattices

Soft Congruence Relations over Rings

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft congruence relations by using the soft set theory. The notions of soft quotient rings, generalized soft ideals and generalized soft quotient rings, are introduced, and several related properties are investigated. Also, we obtain a...

Congruence Relations on Hypergroupoids and Nd-groupoids

In this work we prove that the set of congruences on an nd-groupoid under suitable conditions is a complete lattice which is a sublattice of the lattice of equivalence relations on the nd-groupoid. 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.

Relations among quantum processes: bisimilarity and congruence

Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and distributed quantum computations and quantum communication protocols, communications over quantum channels which move qubits physically from one place to another must ...