See Galois field on Wiktionary
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"text": "The Galois field #x5C;mathrm#x7B;GF#x7D;(pⁿ) has order pⁿ and characteristic p.",
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"text": "The Galois field #x5C;mathrm#x7B;GF#x7D;(pⁿ) is a finite extension of the Galois field #x5C;mathrm#x7B;GF#x7D;(p) and the degree of the extension is n.",
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"text": "The multiplicative subgroup of a Galois field is cyclic.",
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"text": "A Galois field #x5C;mathbb#x7B;F#x7D;#x5F;#x7B;pⁿ#x7D; is isomorphic to the quotient of the polynomial ring #x5C;mathbb#x7B;F#x7D;#x5F;p adjoin x over the ideal generated by a monic irreducible polynomial of degree n. Such an ideal is maximal and since a polynomial ring is commutative then the quotient ring must be a field. In symbols: #x5C;mathbb#x7B;F#x7D;#x5F;#x7B;pⁿ#x7D;#x5C;cong#x7B;#x5C;mathbb#x7B;F#x7D;#x5F;p#x5B;x#x5D;#x5C;over(#x5C;hatf#x5F;n(x))#x7D;.",
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"text": "1958 [Chelsea Publishing Company], Hans J. Zassenhaus, The Theory of Groups, 2013, Dover, unnumbered page,\nA field with a finite number of elements is called a Galois field.\nThe number of elements of the prime field k contained in a Galois field K is finite, and is therefore a natural prime p."
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"ref": "2001, Joseph E. Bonin, A Brief Introduction To Matroid Theory, retrieved 2016-05-05:",
"text": "The case of most interest to us will be that in which F is a finite field, the Galois field GF(q) for some prime power q. If q is prime, this field is #x5C;mathbb#x7B;Z#x7D;#x5F;q, the integers 0,1,#x5C;dots,q-1 with arithmetic modulo q.",
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