# Thread: Terminology for elements in modules

1. ## Terminology for elements in modules

I am looking for an adjective for special elements in modules.

Definition: Let $\displaystyle R$ be a ring and $\displaystyle M$ be an $\displaystyle R$-module.
We say that $\displaystyle v\in M$ is an ????? element if $\displaystyle v=rw$
with $\displaystyle w\in M$ and $\displaystyle r\in R$ implies that $\displaystyle r$ has to be a unit in $\displaystyle R$.

What is the commonly used term ???? for this definition?

In the lattice case $\displaystyle R=\mathbb Z$ and $\displaystyle M=\mathbb Z^N$ these are often called
primitive vectors but this terminology does not seem to be common
for general rings and modules.

Thanks ---

2. Originally Posted by crwtom
I am looking for an adjective for special elements in modules.

Definition: Let $\displaystyle R$ be a ring and $\displaystyle M$ be an $\displaystyle R$-module.
We say that $\displaystyle v\in M$ is an ????? element if $\displaystyle v=rw$
with $\displaystyle w\in M$ and $\displaystyle r\in R$ implies that $\displaystyle r$ has to be a unit in $\displaystyle R$.

What is the commonly used term ???? for this definition?

In the lattice case $\displaystyle R=\mathbb Z$ and $\displaystyle M=\mathbb Z^N$ these are often called
primitive vectors but this terminology does not seem to be common
for general rings and modules.

Thanks ---
why is the terminology important here? if you have a "math" question related to this, you can ask.