ring definition(s)

[franktaw at netscape.net]

>  Certainly the most common definition of a ring does require 
associativity, and does not require a unit. However, this is not 
 >universal. For example, my copy of Birkhoff and MacLane's "Modern 
Algebra" (The MacMillen Company, 1969) does require a >unit.

Sorry, that should be "A Survey of Modern Algebra", published by the 
MacMillan Company.

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