Definition talk:Algebraic Structure

According to this website an algebraic structure is a special case of an algebraic system. The distinction being an algebraic structure is a set together with a set of binary operations whereas an algebraic system is a set together with a set of finitary operations. Would a page on this be good?

http://planetmath.org/AlgebraicSystem.html

I would also like to know if this wiki welcomes definitions and theorems from universal algebra or would prefer if all energy was directed to the sub-disciplines present at the moment.

--Jshflynn 22:38 (BST) 6th June 2012


 * What I (personally) like to guard against is random definitions and proofs. If a discipline is to be developed, then it's good to ensure it's structured.


 * I take your point about an algebraic system being a sort of extension of the concept of algebraic structure, and acknowledge that "universal algebra" could do with being explored here. It would be good if published works could be used as source material, because internet resources are renowned for being ephemeral, inaccurate and changeable.


 * If you have a strategy for documenting universal algebra (something I know nothing about) then I say go for it. --prime mover 18:11, 6 June 2012 (EDT)


 * I would welcome theorems (and corresponding defs) of that generality; they tend to give a broad scope and a solid foundation. Please explore the existing work on model theory and category theory (I recall those areas as being rather brief atm, so that shouldn't be too hard) to find suitable reference hooks to the rest of the site (presuming that you actually want to approach univ. algebra as a branch of model theory, i.e. models without relations). Good luck, I will try to keep up with you, suggesting and asking as comes to my mind. --Lord_Farin 18:19, 6 June 2012 (EDT)