inheritance of module structure

[eisenbud]

If phi: S-->R is a ring homomorphism, M is an S-module and N is an R module, then there is an unambiguous structure of R-module on M\otimes N relative to phi.

In many cases, for example when R has been defined as S/I, one can write map(R,S) in M2 without specifying the map -- that is, there is a "natural" choice.

I suggest that in exactly these cases M**N should be defined as an R-module. More generally, I suggest that one allow a syntax like tensor(phi, M, N) to be the R-module as above.

[DanGrayson]

Sounds good to me.

[mahrud]

Since phi ** M in M2 gives an R-module (here is the documentation), is this the same as phi ** M ** N?

[mahrud]

I believe my last comment means this issue can be closed, but we can reopen it if I'm missing something.

Since phi ** M in M2 gives an R-module (here is the documentation), is this the same as phi ** M ** N?