I study Boolean Algebra and it is clear when: (carrier is a power set, union, intersection), (set of all divisors of n, lcm, gcd), (the set of propositional functions of n given variables, conjunction, disjunction) In all this examples it is easy to see that binary operations on carrier are commutative. It is because structure of a elements of carrier allows it: set does not have order (A union B = B union A), $4*5=5*4$, $prop_1 ∨ prop_2 = prop_2 ∨ prop_1$,…
If we have a set of ordered sequences like $\{(1,2,3), (4,5)…\}$ it is hard for me to imagine commutative binary operations on this set.
Can you please suggest a few examples of Boolean Algebras where carrier is a set of sequences?
I am interested in a simple examples: finite set of strictly increasing, finite sequences. It is not important for a set to contain all sequences. It will be used as examples for teaching.