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Namespace IsNoetherianRing 7 theorems

• Noetherian rings decompose into connected-spectrum idempotent pieces IsNoetherianRing.exists_completeOrthogonalIdempotents_forall_connectedSpace_primeSpectrum 0 below · cited by 1 · depth 16
• Krull–Akizuki for subalgebras of finite extensions IsNoetherianRing.of_ringKrullDim_le_one_of_finiteDimensional_subalgebra 1 below · cited by 3 · depth 31
• Gonflement and completion at a prime of a noetherian ring IsNoetherianRing.exists_faithfullyFlat_isAdicComplete_isAlgClosed_residueField_atPrime 7 below · cited by 2 · depth 32
• Idempotent localisation with no nontrivial idempotents at a prime IsNoetherianRing.exists_isIdempotentElem_notMem_and_forall_isIdempotentElem_away_eq_zero_or_eq_one 0 below · cited by 3 · depth 32
• Globalising an n-th root of unity from geometric points IsNoetherianRing.exists_pow_eq_one_and_forall_apply_eq_of_forall_valuationSubring 0 below · cited by 1 · depth 32
• Noetherian rings: complete families of primitive idempotents IsNoetherianRing.exists_completeOrthogonalIdempotents_forall_mul_eq_zero_or_eq 0 below · cited by 1 · depth 33
• Units of A[1/π] are A^× · π^ℤ IsNoetherianRing.exists_unit_mul_zpow_eq_of_span_singleton_isPrime 0 below · cited by 1 · depth 35