Some articles on ideals, ideal:

Subring Test - Relation To Ideals
... Proper ideals are subrings that are closed under both left and right multiplication by elements from R ... conform to the ring structure, and ideals become subrings ... Ideals may or may not have their own multiplicative identity (distinct from the identity of the ring) The ideal I = {(z,0)
Minimal Prime (commutative Algebra) - Properties
... Every proper ideal I in a commutative ring has at least one minimal prime ideal above it ... Any maximal ideal containing I is prime, and such ideals exist, so the set of prime ideals containing I is non-empty ... The intersection of a decreasing chain of prime ideals is prime ...
Manhauling - Modern Perspective - Ideals
... Similar to the modern, fast, free, and equipment light Alpine climbing ideals, modern manhaul purists seek to achieve mileage on their journey where ...

Famous quotes containing the word ideals:

    The real weakness of England lies, not in incomplete armaments or unfortified coasts, not in the poverty that creeps through sunless lanes, or the drunkenness that brawls in loathsome courts, but simply in the fact that her ideals are emotional and not intellectual.
    Oscar Wilde (1854–1900)

    But I would emphasize again that social and economic solutions, as such, will not avail to satisfy the aspirations of the people unless they conform with the traditions of our race, deeply grooved in their sentiments through a century and a half of struggle for ideals of life that are rooted in religion and fed from purely spiritual springs.
    Herbert Hoover (1874–1964)

    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)