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.

I have also seen a definition of subring which requires that, if the 
ring has a unit, the subring has the same unit. This raises the bizarre 
possibility that for three rings R, S, and T, R is a subring of S, 
which is a subring of T, but R is not a subring of T.

Best to stick with the most standard definition, but do be aware that 
there are others in use.  (A phrase like "non-associative ring" is 
sufficient to indicate that the standard definition of ring is not 
being used.)

 -----Original Message-----
 From: Creighton Dement <crowdog at crowdog.de>

  A sci.math thread recently mentioned the difference in the definition 
of
 a ring given at Mathworld http://mathworld.wolfram.com/Ring.html and
 Wikipedia http://en.wikipedia.org/wiki/Ring_theory : the former
 specifies that multiplication defined for a ring not necessarily be
 associative; the latter specifies not only that multiplication be
 associative, but that it must also have a unit (this part of the
 definition seems unusual to me).




___________________________________________________
Try the New Netscape Mail Today!
Virtually Spam-Free | More Storage | Import Your Contact List
http://mail.netscape.com