Universal algebra is the set equipped with set of operations of different arity. Usually we consider that sum or product are between these operations. this is natural consequence of our experience. However we may assume that there exists algebra which does not have sum and product in list of operations. Even this is unusual, probably somebody saw in his practice such type of algebra. For me will be interesting if you can share such experience.
I thank everybody who answered my question and will try to answer all ideas. My question was if there exists algebra which does not have sum and product in the list of operations. I think one of such algebras may be Boolean algebra, but maybe there exist other interesting algebras.
Mohamed. Even non commutative algebra assumes non commutative product, your post is interesting for me. I do some research in non commutative algebra and for me is interesting how I can apply it in the physics. We can discuss this problem as well.
Peter. Peano arithmetic or Peano axioms means set of natural numbers, and this set is equipped by sum and product. However, from your post, I think you have in mind something different.
Working with my current paper I found universal algebra which does not have product and sum. If we consider lattice, then this set with operation min and max can be considered as universal algebra.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Quantum Physics
- Quantum Mechanics