[FOM] Identities

[A. Mani]

On Sunday 21 Jan 2007 23:33, Dana Scott wrote:
> Take any equational theory with an unsolvable word
> problem (e.g., monoids, groups, rings, lattices).
>
> Then take as identities the axioms of the theory plus
> a number of equations between constants (i.e., thinking
> of generators and relations).
>
> Hence, the problem of deducing another equation (without
> variables, a special kind of identity) is exactly the
> original word problem for the theory.

This can be extended to weak identities as well (of some forms). For example 
see Crvenkovic, S. et al ´on a problem of partial algebras´ Rev. Res. Math. 
ser. 17,2, 39--55 (1989). (Novisad J Math)


A. Mani
Member, Cal. Math. Soc