Compatible Operation
Let A be a set (of the elements of an algebra ), and let E be an equivalence relation on the set A. The relation E is said to be compatible with (or have the substitution property with respect to) an n-ary operation f if for all whenever implies . An equivalence relation compatible with all the operations of an algebra is called a congruence.
Read more about this topic: Quotient Algebra
Famous quotes containing the words compatible and/or operation:
“As to happiness in this life it is hardly compatible with that diminished respect which ever attends the relinquishing of labour.”
—Anthony Trollope (1815–1882)
“Human knowledge and human power meet in one; for where the cause is not known the effect cannot be produced. Nature to be commanded must be obeyed; and that which in contemplation is as the cause is in operation as the rule.”
—Francis Bacon (1560–1626)