In commutative algebra, the extension and contraction of ideals are operations performed on sets of ideals.
Other articles related to "extension and contraction of ideals, extension, ideal":
... Let K be a field extension of L, and let B and A be the rings of integers of K and L, respectively ... Then B is an integral extension of A, and we let f be the inclusion map from A to B ... The behaviour of a prime ideal of A under extension is one of the central problems of algebraic number theory ...
Famous quotes containing the words ideals and/or extension:
“We want our children to become warm, decent human beings who reach out generously to those in need. We hope they find values and ideals to give their lives purpose so they contribute to the world and make it a better place because they have lived in it. Intelligence, success, and high achievement are worthy goals, but they mean nothing if our children are not basically kind and loving people.”
—Neil Kurshan (20th century)
“A dense undergrowth of extension cords sustains my upper world of lights, music, and machines of comfort.”
—Mason Cooley (b. 1927)