Definition of algebraic structure Is there a definition of _algebraic structure_? Wikipedia says: > a set (called carrier set or underlying set) with one or more finitary operations defined on it. In particular, what is the motivation to say that a lattice is an algebraic structure, but not saying that a poset is an algebraic structure? Are they too boring? Referring to wikipedia, the term "one or more finitary operations" seems to hold for almost everything I know.

A poset has a structure, but not an algebraic structure. A poset is equipped with a partial order relation, this is not a finitary operation. For a set $S$ an $n$-tary operation is a function $F:S^n\to S$. An order relation is not a function.