wedge product of a module

Let \(R\) be a commutative ring and \(M\) an \(R\)-module. Then the exterior algera \(\bigwedge^n E\) is defined as quotient module

\begin{align*} \bigwedge^n E = (\bigotimes_{i=1}^n E)/ \langle U\rangle \end{align*}

with

\begin{align*} U = \{v_1 \otimes ... \otimes v_n \vert v_r = v_s, 1 \leq r < s \leq n\} \end{align*}