Module ** Ring -- tensor product

Synopsis

Operator: **
Usage:

M ** R

R ** M

tensor(M, R)

tensor(R, M)
Inputs:
- M, a module, a module or an ideal,
- R, a ring,
Outputs:
- a module, 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