Revision #551 → #1224 · back to history
addedFinite field5a7c62e5da1a
addedOrder of a finite field5f4b62d0e2b4
addedExistence and isomorphism of finite fields by order1451f3a3c8b4
addedOrder/size of a finite field (Properties)f7195db03113
addedCharacterization of orders of finite fieldscfefc57ce4a6
addedUniqueness of finite fields of given order494efb277eff
addedPolynomial X^q - X has all elements as roots33b1d4efbdf5
addedMultiplicative group of a finite field is cyclic0eebcc5f46b2
addedPrimitive element1e9b71ac638a
addedPrime fields as integers modulo p14d9e4cecbf5
addedCharacteristic of a finite field3bf9093171b6
addedFreshman's dream identity157ee12b9b2e
addedFermat's little theorem for finite fieldsb6611cb7337b
addedFinite fields are perfect (separable simple extensions)e334f9eefbb0
addedChevalley–Warning: finite fields are quasi-algebraically closed28a1a508753a
addedSplitting field of X^q - X has order q06568ecb5093
addedUniqueness up to isomorphism via splitting fieldsd81bf196db30
addedMoore's classification theorem for finite fields9e5b144d897a
addedSubfield criterion for finite fieldsebb686bdc0fe
addedConstruction of GF(p^n) via irreducible polynomial quotiented434a4522ec
addedField with four elements GF(4)40a99dbb5620
addedFrobenius automorphism on GF(4)db5ab40ef482
addedIrreducibility of X^2 - r over GF(p) via quadratic non-residuea8a8c3d3f71c
addedConstruction of GF(p^2) for odd prime p3007b791e594
addedConstruction of GF(8) and GF(27)c373a0916052
addedConstruction of GF(16)1c8b9c00df53
addedPrimitive elements of GF(16)11fe2ca09a34
addedMultiplicative group of a finite field is cyclicdc536d0f27ec
addedPrimitive element of GF(q)7126616fa3c2
addedNumber of primitive elements via Euler's totient06e8023a58f7
addedDiscrete logarithmb83b85c124a6
addedZech's logarithms2007398cdf36
addedEvery nonzero element is a root of unity7c4f489e0973
addedn-th primitive root of unity20419c65a5f2
addedExistence criterion for primitive n-th roots of unity in GF(q)7df0e8b00ca9
addedNo primitive p-th roots of unity in characteristic p817f436cac78
addedCyclotomic polynomial factorization in characteristic p939ed7da530b
addedGF(64) subfields and primitive elements0132a9a8b9c6
addedFrobenius automorphism7101e2d8422d
addedPowers of Frobenius and order n72bc87bc95f0
addedGalois group of GF(p^n)/GF(p) is cyclic of order nb0f393b69844
addedEvery finite field is perfect (via surjective Frobenius)bfae5a2b6515
addedIrreducible polynomial over a finite fieldad58cbc3b19b
addedUnique factorization of monic polynomials over finite fieldsa58ca5c10f80
addedX^q - X is product of all monic degree-one polynomialsdf93be0f0648
addedX^q - X is product of irreducible monic polynomials of degree dividing nbb49e79d4583
addedNumber of monic irreducible polynomials of degree n over GF(q)c6dc9ccf00d0
addedExistence of irreducible polynomial of every degree999681673588
addedFinite fields are not algebraically closedcc8288fcd9f7
addedAlgebraic closure of GF(p) and its structure626f83cccb7c
addedUnique degree-n subextension of the algebraic closure2cf49cf17f40
addedAlgebraic closure as direct limit79333a9b7df9
addedWedderburn's little theoremf9e27fbb3dbd
addedArtin–Zorn theorem8a6c69e3ac10