History of Field

	Revision 51 . . December 14, 2001 10:13 pm by Zundark [prime subfield]
	Revision 50 . . December 14, 2001 4:41 am by AxelBoldt [+subfield]
	Revision 49 . . December 14, 2001 4:36 am by AxelBoldt [+subfield]
	Revision 48 . . December 14, 2001 4:35 am by AxelBoldt [+subfield]
	Revision 47 . . December 14, 2001 4:31 am by AxelBoldt [+subfield]
	Revision 46 . . December 10, 2001 2:06 pm by AxelBoldt
	Revision 45 . . December 10, 2001 2:04 pm by AxelBoldt
	Revision 44 . . December 10, 2001 6:16 am by AxelBoldt [+field homomorphisms]
	Revision 43 . . December 10, 2001 1:16 am by AxelBoldt [finite subgroups of (F-{0}, *)]
	Revision 42 . . December 9, 2001 6:37 am by AxelBoldt [+characteristic, algebraic closure, Frobenius homomorphism]
	Revision 41 . . December 9, 2001 6:35 am by AxelBoldt [+characteristic, algebraic closure, Frobenius homomorphism]
	Revision 40 . . December 9, 2001 6:32 am by AxelBoldt [+characteristic, algebraic closure, Frobenius homomorphism]
	Revision 39 . . December 9, 2001 6:32 am by AxelBoldt [+characteristic, algebraic closure, Frobenius homomorphism]
	Revision 38 . . December 9, 2001 6:29 am by AxelBoldt [+characteristic, algebraic closure, Frobenius homomorphism]
	Revision 37 . . December 9, 2001 6:02 am by AxelBoldt [link to finite field]
	Revision 36 . . November 19, 2001 8:50 am by AxelBoldt [+p-adic numbers]
	Revision 35 . . October 15, 2001 2:26 am by Josh Grosse [Modular arithmetics are not the only finite fields]

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Difference (from prior major revision) (no other diffs)

Changed: 83,84c83,87

Every field of characteristic 0 contains a copy of the rationals Q and is therefore infinite; every field of characteristic p contains a copy of Zp. There are finite fields and infinite fields of characteristic p.

Every field has a unique smallest subfield, which is called the prime subfield and is contained in every other subfield. For fields of characteristic 0, the prime subfield is isomorphic to Q (the rationals). Fields of characteristic 0 are therefore always infinite. For fields of prime characteristic p, the prime subfield is isomorphic to Zp. Fields of prime characteristic can be either infinite or finite (see Finite field).

Removed: 87d89