Namespace IsArtinianRing 11 theorems
- Artinian local ring with finite residue field is finite
IsArtinianRing.finite_of_finite_residueField0 below · cited by 1 · depth 10 - Artinian localisation at non-zero-divisors is the total quotient ring
IsArtinianRing.isLocalization_nonZeroDivisors_of_isLocalization_of_le_nonZeroDivisors0 below · cited by 1 · depth 27 - Artin local covers with algebraically closed residue field
IsArtinianRing.exists_faithfullyFlat_isLocalHom_isAlgClosed_residueField_of_finite_residueField6 below · cited by 1 · depth 30 - Hilbert's Theorem 90 for a free cyclic action
IsArtinianRing.exists_units_eq_mul_apply_of_prod_iterate_apply_eq_one0 below · cited by 1 · depth 30 - Base change of a finite Artin local ring along a flat ℤ-algebra
IsArtinianRing.flat_and_finite_and_isNoetherianRing_tensorProduct_int_of_finite_residueField0 below · cited by 1 · depth 31 - Residue fields of C⊗_ℤO are algebraically closed of characteristic ℓ
IsArtinianRing.isAlgClosed_residueField_of_isMaximal_tensorProduct_int_of_isAlgClosed_residueField1 below · cited by 1 · depth 31 - Reducedness of the fibre of C ⊗_ℤ O over mathfrak m_C
IsArtinianRing.isReduced_and_isArtinianRing_tensorProduct_int_quotient_map_maximalIdeal0 below · cited by 1 · depth 31 - An Artinian local ring with finite residue field is finite
IsArtinianRing.finite_of_isLocalRing_of_finite_residueField0 below · cited by 1 · depth 32 - Gonflement of an Artinian local ring
IsArtinianRing.exists_isArtinianRing_faithfullyFlat_map_maximalIdeal_eq_isAlgClosed_residueField3 below · cited by 1 · depth 35 - Artinian ring: A/n^N≅ Aₙ when J(A)^N=0
IsArtinianRing.nonempty_quotient_pow_algEquiv_localization_atPrime0 below · cited by 1 · depth 37 - Nonzero socle element in an Artinian local ring
IsArtinianRing.exists_ne_zero_mem_maximalIdeal_forall_mul_eq_zero0 below · cited by 1 · depth 41