History of Boolean algebra

	Revision 13 . . December 9, 2001 7:29 am by AxelBoldt
	Revision 12 . . December 9, 2001 6:54 am by Taw [that is a+b=a xor b]
	Revision 11 . . December 1, 2001 12:32 am by AxelBoldt [homomorphisms and isomorphisms]
	Revision 10 . . December 1, 2001 12:31 am by AxelBoldt [homomorphisms and isomorphisms]
	Revision 9 . . November 30, 2001 8:45 am by AxelBoldt [examples, finite boolean algebras, representation theorem]
	Revision 8 . . (edit) August 23, 2001 4:52 am by Zundark [fix link]

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by defining a + b = (a ^ ~b) v (b ^ ~a) (that is a+b=a XOR? b) and a * b = a ^ b. This ring has the property that a * a = a for all a in A; rings like that are called Boolean rings. One can show that every Boolean ring arises from a Boolean algebra, and vice versa: the categories of Boolean rings and Boolean algebras are equivalent.

by defining a + b = (a ^ ~b) v (b ^ ~a) (this operation is called "symmetric difference" in the case of sets and XOR in the case of logic) and a * b = a ^ b. This ring has the property that a * a = a for all a in A; rings like that are called Boolean rings. One can show that every Boolean ring arises from a Boolean algebra, and vice versa: the categories of Boolean rings and Boolean algebras are equivalent.