Talk:Cancellable iff Regular Representations Injective

I can't see how this proof isn't applicable to magmas in general and I need that to be the case for another proof I am making. Correct if necessary. --Jshflynn 07:45, 20 July 2012 (UTC)

In most treatments of abstract algebra, the Regular Representations are defined and used only in the context of the associative operator. The definition pages for R.R.R and L.R.R. themselves are therefore defined in the context of Semigroup, and the citations given refer to expositions with exactly that restriction.

Two things will need to be done:

(a) All the pages defining R.R's and proving results on them will need to be re-assessed as to whether the results still stand for magmas;

(b) A note needs to be added to the various pages indicating the usual understanding that in most contexts it is understood that the structure in question is a magma.

In fact, does it need to be a magma? Can it be any general algebraic structure which does not even need to be a magma? --prime mover 07:56, 20 July 2012 (UTC)

The problems emerge in showing that the RR is in fact a representation (a homomorphism), where associativity is needed. The statement of this page in particular is applicable to any alg. structure. --Lord_Farin 14:43, 20 July 2012 (UTC)