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All quotient rings of a Noetherian ring are Noetherian, but that does not automatically keep for its subrings. The chain issue also may be inherited by mixtures or extensions of a Noetherian object. For example, finite immediate sums of Noetherian rings are Noetherian, as will be the ring of formal electricity series about a Noetherian ring.
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In her 1926 paper,[114] Noether extended Hilbert's theorem to representations of a finite team in excess of any discipline; The brand new case that did not observe from Hilbert's perform is once the attribute of the sphere divides the purchase of your team. Noether's consequence was afterwards extended by William Haboush to all reductive groups by his proof in the Mumford conjecture.
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For example, there is a team which represents the rigid rotations of Place. It is a style of symmetry of House, because Area by itself would not change when it really is rotated Despite the fact that the positions of objects in it do. Noether applied these forms of symmetries in her work on invariants in physics.
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