# Module ** Ring -- tensor product

## Synopsis

• Operator: **
• Usage:
M ** R
R ** M
• Inputs:
• Outputs:
• , over R, obtained by forming the tensor product of the module M with R

## Description

If the ring of M is a base ring of R, then the matrix presenting the module will be simply promoted (see promote). Otherwise, a ring map from the ring of M to R will be constructed by examining the names of the variables, as described in map(Ring,Ring).
 i1 : R = ZZ/101[x,y]; i2 : M = coker vars R o2 = cokernel | x y | 1 o2 : R-module, quotient of R i3 : M ** R[t] o3 = cokernel | x y | 1 o3 : R[t]-module, quotient of (R[t])

## Ways to use this method:

• "Ideal ** Ring"
• Module ** Ring -- tensor product
• "Ring ** Ideal"
• "Ring ** Module"