Let $(M,\cdot)$ be a magma. Does the property $(x\cdot y)\cdot(z\cdot t) = x\cdot(y\cdot z)\cdot t$ have a special name? Thanks.

  • 12
    What does the right-hand side mean? It's lacking a pair of parentheses. – Gro-Tsen Dec 6 at 20:11
  • If the magma has a unit, or satisfies the identity x*x=x, this is just associativity (regardless of which way you group x(yz)t). If you have a left or right band or rectangular band, the identities are consequences of band identities. I think you have three distinct magma varieties depending on which subset of groupings of x(yz)t you adopt. Starting with the linked article on magmas is a good idea. Gerhard "Searching 'Generalized Associativity' Might Help" Paseman, 2018.12.06. – Gerhard Paseman Dec 6 at 21:17

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.