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:
“God isn’t compatible with machinery and scientific medicine and universal happiness. You must make your choice. Our civilization has chosen machinery and medicine and happiness.”
—Aldous Huxley (1894–1963)
“Waiting for the race to become official, he began to feel as if he had as much effect on the final outcome of the operation as a single piece of a jumbo jigsaw puzzle has to its predetermined final design. Only the addition of the missing fragments of the puzzle would reveal if the picture was as he guessed it would be.”
—Stanley Kubrick (b. 1928)