Revision #2490 → #3915 · back to history
addedAlgebraically closed field429720a72541
addedFundamental theorem formulation17d2a521b027
addedReal numbers not algebraically closed5e62f6bdcd21
addedComplex numbers algebraically closedca1638d5e375
addedAlgebraic closure exists060d03a14077
addedAlgebraic closure42000348a69f
addedAlgebraic closure uniqueness9275bcb6011f
addedAlgebraically closed fields in class hierarchy386ec2cbe1b5
addedReal numbers example5caefbd20909
addedNo real subfield is algebraically closed91c81642de77
addedRational numbers not algebraically closedaaab7c1d688f
addedFundamental theorem of algebra575c4a86a3ba
addedAlgebraic numbers algebraically closeda11dcbd2e97a
addedNo finite field is algebraically closeda12e8a12e7e6
addedUnion of finite fields fixed characteristicae153a3b22f1
addedAlgebraic closure of finite field794b639b3ec7
addedComplex rational function field not algebraically closed225443853a58
addedSquare root rational function roots absent36de8f7833cc
addedAlgebraic closedness has equivalent assertionscd0fcad2ecc9
addedIrreducible polynomials have degree onef1e1d1cb0b23
addedLinear polynomials irreducible556a1428b8bd
addedIrreducible polynomial over algebraically closed field is linear1adc8054d783
addedNon-algebraically closed field has irreducible polynomial of degree greater than one4d7e8b5bf0cc
addedIrreducible factor of rootless polynomial has no roots28b0a877035c
addedFirst degree polynomial has a root12b9f029577c
addedPolynomial splitting criterion6a6157840922
addedLinear factor form64e7845660ce
addedRoot from splitting property1ec05c327142
addedFactorization into irreducibles5d9bfeb51925
addedPrime degree root criterion46b690b9e599
addedAlgebraically closed iff prime degree roots224241aa3047
addedNo proper algebraic extension criterionbcdcfea9b8e4
addedQuotient by irreducible polynomial is algebraic extension78617c157c5e
addedProper algebraic extension contains element with nonlinear minimal polynomial70bf85751e63
addedNo proper finite extension criterionca6f2b6c6376
addedFinite extensions algebraica9c32027ae1f
addedEigenvector criterion643bc97c2d34
addedEigenvector iff characteristic polynomial has root944c61ca8c9b
addedAlgebraic closedness gives eigenvectors8e712d12321b
addedMonic rescaling preserves rootsa5ff8b0a102e
addedCompanion matrix characteristic polynomial9d17ca1da656
addedPartial fractions criterion385ff539facd
addedPartial fractions over algebraically closed fields94263b6bb53a
addedPartial fractions force irreducibles linear4368319a4b36
addedDenominator product of linear polynomials837057705221
addedRelatively prime polynomials have no common root23c5755b0977
addedCommon-root converse characterizes algebraically closed fieldsd869ba4b4a81
addedNon-coprime polynomials over algebraically closed field have common roota4edb40777c7
addedNon-algebraically closed counterexample to common-root converse64866e556182
addedAlgebraically closed fields contain roots of unitye97bc4a5ef88
addedCyclotomic extension44ece4632d2d
addedCyclotomic closure15f8e406a063
addedAlgebraically closed fields cyclotomically closed09754f7df75d
addedCyclotomically closed converse falsebbb93dc79b0f
addedBinomial splitting insufficientf7163e2f3095
addedFirst-order transfer for same characteristicb8aab5054658
addedLefschetz principle finite characteristic bound22ec74ec1801
addedAlgebraically closed extension existsd318f04c66ad
addedAlgebraically closed extensiond62197bfd088
addedAlgebraic closure existence and uniquenessb81d5ed68fd2
addedAlgebraic closure of a fieldd8cb78bbb4d9
addedQuantifier elimination for algebraically closed fieldsfb72fb8ca62f
addedNo algebraically closed finite field9676b6ffbc67