Example 14.34.6. In Example 14.34.4 we have X_ n(M) = R[R[\ldots [M]\ldots ]] with n + 1 brackets. We describe the maps constructed above using a typical element
\xi = \sum \nolimits _ i r_ i\left[\sum \nolimits _ j r_{ij}[m_{ij}]\right]
of X_1(M). The maps d_0, d_1 : R[R[M]] \to R[M] are given by
d_0(\xi ) = \sum \nolimits _{i, j} r_ ir_{ij}[m_{ij}] \quad \text{and}\quad d_1(\xi ) = \sum \nolimits _ i r_ i\left[\sum \nolimits _ j r_{ij}m_{ij}\right].
The maps s_0, s_1 : R[R[M]] \to R[R[R[M]]] are given by
s_0(\xi ) = \sum \nolimits _ i r_ i\left[\left[\sum \nolimits _ j r_{ij}[m_{ij}]\right]\right] \quad \text{and}\quad s_1(\xi ) = \sum \nolimits _ i r_ i\left[\sum \nolimits _ j r_{ij}[[m_{ij}]]\right].
Comments (0)
There are also: