# A magma with the property (xy)(zt) = x(yz)t

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.

• 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