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Noetherian ring Isomorphism theorems Dedekind domain Hilbert's basis theorem Differential algebra Ideal class group Principal ideal Fundamental theorem of arithmetic Levi decomposition Prime element Primary ideal Lefschetz fixed-point theorem Generating set of a group Spectrum of a ring Cartan decomposition Euclidean domain Regular local ring Invariant basis number Frobenius endomorphism Lie's third theorem Pontryagin duality Semisimple lie algebra Cayley's theorem Unique factorization domain Sum of two squares theorem Lattice Modularity theorem Ascending chain condition Lattice of subgroups Radical of an ideal Maximal ideal Incidence algebra Fundamental representation Lie algebra representation Lefschetz hyperplane theorem Fundamental group Schur product theorem Quadratic reciprocity Chen's theorem Intersection theory Ring theory Perfect group Quotient ring Dual space Compact operator on hilbert space Normal extension Group of lie type Poisson algebra Finite intersection property Artinian ring Hurewicz theorem Finitely generated group Hasse principle Partition Representation theorem Commutative algebra Maschke's theorem Geometric lattice Finitely generated abelian group Class field theory Lie algebra extension Finitely generated algebra Frobenius algebra Noether's theorem Grothendieck group Legendre function Aliquot sum Convolution theorem P-group Affine group Complexification Newton's identities Constructible universe Splitting field Borel set Arithmetic derivative Subring Primitive element theorem Polynomial ring Directed set Conjugacy class Noether's second theorem Dirichlet's approximation theorem Polycyclic group Isometry group Characteristic Tietze extension theorem Local ring Cantor's theorem Projective variety Divisible group Explicit formulae for l-functions Analytic function of a matrix Ring of integers Algebra of sets Krull dimension Nakayama's lemma Matrix ring Partition of a set Partial fraction decomposition

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