"Ideals were introduced first by Marshall H. Stone, who derived their name from the ring ideals of abstract algebra. He adopted this terminology because, using the isomorphism of the categories of Boolean algebras and of Boolean rings, both notions do indeed coincide."
For these ideals we have a dual notion -- filters. Can one pull that duality back to ring and algebra ideals?
soyka62 has a great collection of pictures. This one is presumably Yves Decoste: