What do you call a semimodule in which the product of a non-zero vector by a non-zero scalar isn't zero?

Question

Given a semiring $R$, a left $R$-semimodule consists of an additively-written commutative monoid $M$ and a map from $R \times M$ to $M$ satisfying the following axioms:

1. $r (m + n) = rm + rn$
2. $(r + s) m = rm + sm$
3. $(rs)m = r(sm)$
4. $1_Rm = m$
5. $0_R m = r 0_M = 0_M$

Is there a name for a left $R$-semimodule, which satisfies the following additional axiom?

6. If $rm = 0_M$, either $r = 0_R$ or $m = 0_M$.

Is there a name for the property described in axiom 6 (so I can look it up in a textbook or with Google)?

Answer 1

As commented, torsion-free module is an standard name. This name is used for groups very frequently, too.