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These theorems enable a single to classify all finite-dimensional central division algebras about a supplied selection area. A subsequent paper by Noether confirmed, for a Specific circumstance of a far more standard theorem, that each one maximal subfields of a division algebra D are splitting fields.
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Noether's advisor, Paul Gordan, was called the "king of invariant theory", and his chief contribution to arithmetic was his 1870 Answer from the finite foundation challenge for invariants of homogeneous polynomials in two variables.[ninety one][ninety two] He proved this by offering a constructive approach for locating most of the invariants as well as their turbines, but was not able to carry out this constructive approach for invariants in three or maybe more variables.
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In 1943, French mathematician Claude Chevalley coined the phrase, Noetherian ring, to describe this home.[105] A serious cause Noether's 1921 paper would be the Lasker–Noether theorem, which extends Lasker's theorem on the key decomposition of beliefs of polynomial rings to all Noetherian rings. The Lasker–Noether theorem may be considered like a generalization of the basic theorem of arithmetic which states that any beneficial integer is usually expressed as an item of key quantities, and this decomposition is exclusive.