Quotient Algebra - Compatible Operation

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:

    I have no ambition to surprise my reader. Castles with unknown passages are not compatible with my homely muse.
    Anthony Trollope (1815–1882)

    It requires a surgical operation to get a joke well into a Scotch understanding. The only idea of wit, or rather that inferior variety of the electric talent which prevails occasionally in the North, and which, under the name of “Wut,” is so infinitely distressing to people of good taste, is laughing immoderately at stated intervals.
    Sydney Smith (1771–1845)