If we fix a specific ring "R", we can consider the class of left "R-"modules. To express the scalar multiplication with elements from "R", we need one unary operation for each element of "R." If the ring is infinite, we will thus have infinitely many operations, which is allowed by the definition of an algebraic structure in universal algebra. We will then also need infinitely many identities to express the module axioms, which is allowed by the definition of a variety of algebras. So the left "R"-modules do form a variety of algebras.